diff --git a/docs/mathgenerator/_gen_list.html b/docs/mathgenerator/_gen_list.html index 1a85f5e..a74e4c1 100644 --- a/docs/mathgenerator/_gen_list.html +++ b/docs/mathgenerator/_gen_list.html @@ -214,7 +214,8 @@ 136 ("kinetic_energy", "physics"), 137 ("potential_dividers", "physics"), 138 ("resistivity", "physics"), -139] +139 ("fringe_spacing", "physics"), +140] @@ -223,7 +224,7 @@
gen_list = - [('addition', 'basic_math'), ('subtraction', 'basic_math'), ('multiplication', 'basic_math'), ('division', 'basic_math'), ('binary_complement_1s', 'computer_science'), ('modulo_division', 'computer_science'), ('square_root', 'basic_math'), ('power_rule_differentiation', 'calculus'), ('square', 'basic_math'), ('lcm', 'misc'), ('DELETED', 'DELETED'), ('basic_algebra', 'algebra'), ('log', 'algebra'), ('fraction_to_decimal', 'basic_math'), ('decimal_to_binary', 'computer_science'), ('binary_to_decimal', 'computer_science'), ('divide_fractions', 'basic_math'), ('multiply_int_to_22_matrix', 'algebra'), ('area_of_triangle', 'geometry'), ('valid_triangle', 'geometry'), ('midpoint_of_two_points', 'algebra'), ('factoring', 'algebra'), ('third_angle_of_triangle', 'geometry'), ('system_of_equations', 'algebra'), ('distance_two_points', 'algebra'), ('pythagorean_theorem', 'geometry'), ('linear_equations', 'algebra'), ('prime_factors', 'misc'), ('fraction_multiplication', 'basic_math'), ('angle_regular_polygon', 'geometry'), ('combinations', 'statistics'), ('factorial', 'basic_math'), ('surface_area_cube', 'geometry'), ('surface_area_cuboid', 'geometry'), ('surface_area_cylinder', 'geometry'), ('volume_cube', 'geometry'), ('volume_cuboid', 'geometry'), ('volume_cylinder', 'geometry'), ('surface_area_cone', 'geometry'), ('volume_cone', 'geometry'), ('common_factors', 'misc'), ('intersection_of_two_lines', 'algebra'), ('permutation', 'statistics'), ('vector_cross', 'algebra'), ('compare_fractions', 'basic_math'), ('simple_interest', 'algebra'), ('matrix_multiplication', 'algebra'), ('cube_root', 'basic_math'), ('power_rule_integration', 'calculus'), ('fourth_angle_of_quadrilateral', 'geometry'), ('quadratic_equation', 'algebra'), ('DELETED', 'DELETED'), ('dice_sum_probability', 'statistics'), ('exponentiation', 'basic_math'), ('confidence_interval', 'statistics'), ('surds_comparison', 'misc'), ('fibonacci_series', 'computer_science'), ('basic_trigonometry', 'geometry'), ('sum_of_polygon_angles', 'geometry'), ('data_summary', 'statistics'), ('surface_area_sphere', 'geometry'), ('volume_sphere', 'geometry'), ('nth_fibonacci_number', 'computer_science'), ('profit_loss_percent', 'misc'), ('binary_to_hex', 'computer_science'), ('multiply_complex_numbers', 'algebra'), ('geometric_progression', 'misc'), ('geometric_mean', 'misc'), ('harmonic_mean', 'misc'), ('euclidian_norm', 'misc'), ('angle_btw_vectors', 'geometry'), ('absolute_difference', 'basic_math'), ('vector_dot', 'algebra'), ('binary_2s_complement', 'computer_science'), ('invert_matrix', 'algebra'), ('sector_area', 'geometry'), ('mean_median', 'statistics'), ('int_matrix_22_determinant', 'algebra'), ('compound_interest', 'algebra'), ('decimal_to_hexadeci', 'computer_science'), ('percentage', 'basic_math'), ('celsius_to_fahrenheit', 'misc'), ('arithmetic_progression_term', 'misc'), ('arithmetic_progression_sum', 'misc'), ('decimal_to_octal', 'computer_science'), ('decimal_to_roman_numerals', 'misc'), ('degree_to_rad', 'geometry'), ('radian_to_deg', 'geometry'), ('trig_differentiation', 'calculus'), ('definite_integral', 'calculus'), ('is_prime', 'basic_math'), ('bcd_to_decimal', 'computer_science'), ('complex_to_polar', 'misc'), ('set_operation', 'misc'), ('base_conversion', 'misc'), ('curved_surface_area_cylinder', 'geometry'), ('perimeter_of_polygons', 'geometry'), ('power_of_powers', 'basic_math'), ('quotient_of_power_same_base', 'misc'), ('quotient_of_power_same_power', 'misc'), ('complex_quadratic', 'algebra'), ('is_leap_year', 'misc'), ('minutes_to_hours', 'misc'), ('decimal_to_bcd', 'computer_science'), ('circumference', 'geometry'), ('combine_like_terms', 'algebra'), ('signum_function', 'misc'), ('conditional_probability', 'statistics'), ('arc_length', 'geometry'), ('binomial_distribution', 'misc'), ('stationary_points', 'calculus'), ('expanding', 'algebra'), ('area_of_circle', 'geometry'), ('volume_cone_frustum', 'geometry'), ('equation_of_line_from_two_points', 'geometry'), ('area_of_circle_given_center_and_point', 'geometry'), ('factors', 'misc'), ('volume_hemisphere', 'geometry'), ('percentage_difference', 'basic_math'), ('percentage_error', 'basic_math'), ('greatest_common_divisor', 'basic_math'), ('product_of_scientific_notations', 'misc'), ('volume_pyramid', 'geometry'), ('surface_area_pyramid', 'geometry'), ('is_composite', 'basic_math'), ('complementary_and_supplementary_angle', 'geometry'), ('simplify_square_root', 'basic_math'), ('line_equation_from_2_points', 'algebra'), ('orthogonal_projection', 'algebra'), ('area_of_trapezoid', 'geometry'), ('tribonacci_series', 'computer_science'), ('nth_tribonacci_number', 'computer_science'), ('velocity_of_object', 'misc'), ('binary_addition', 'computer_science'), ('kinetic_energy', 'physics'), ('potential_dividers', 'physics'), ('resistivity', 'physics')] + [('addition', 'basic_math'), ('subtraction', 'basic_math'), ('multiplication', 'basic_math'), ('division', 'basic_math'), ('binary_complement_1s', 'computer_science'), ('modulo_division', 'computer_science'), ('square_root', 'basic_math'), ('power_rule_differentiation', 'calculus'), ('square', 'basic_math'), ('lcm', 'misc'), ('DELETED', 'DELETED'), ('basic_algebra', 'algebra'), ('log', 'algebra'), ('fraction_to_decimal', 'basic_math'), ('decimal_to_binary', 'computer_science'), ('binary_to_decimal', 'computer_science'), ('divide_fractions', 'basic_math'), ('multiply_int_to_22_matrix', 'algebra'), ('area_of_triangle', 'geometry'), ('valid_triangle', 'geometry'), ('midpoint_of_two_points', 'algebra'), ('factoring', 'algebra'), ('third_angle_of_triangle', 'geometry'), ('system_of_equations', 'algebra'), ('distance_two_points', 'algebra'), ('pythagorean_theorem', 'geometry'), ('linear_equations', 'algebra'), ('prime_factors', 'misc'), ('fraction_multiplication', 'basic_math'), ('angle_regular_polygon', 'geometry'), ('combinations', 'statistics'), ('factorial', 'basic_math'), ('surface_area_cube', 'geometry'), ('surface_area_cuboid', 'geometry'), ('surface_area_cylinder', 'geometry'), ('volume_cube', 'geometry'), ('volume_cuboid', 'geometry'), ('volume_cylinder', 'geometry'), ('surface_area_cone', 'geometry'), ('volume_cone', 'geometry'), ('common_factors', 'misc'), ('intersection_of_two_lines', 'algebra'), ('permutation', 'statistics'), ('vector_cross', 'algebra'), ('compare_fractions', 'basic_math'), ('simple_interest', 'algebra'), ('matrix_multiplication', 'algebra'), ('cube_root', 'basic_math'), ('power_rule_integration', 'calculus'), ('fourth_angle_of_quadrilateral', 'geometry'), ('quadratic_equation', 'algebra'), ('DELETED', 'DELETED'), ('dice_sum_probability', 'statistics'), ('exponentiation', 'basic_math'), ('confidence_interval', 'statistics'), ('surds_comparison', 'misc'), ('fibonacci_series', 'computer_science'), ('basic_trigonometry', 'geometry'), ('sum_of_polygon_angles', 'geometry'), ('data_summary', 'statistics'), ('surface_area_sphere', 'geometry'), ('volume_sphere', 'geometry'), ('nth_fibonacci_number', 'computer_science'), ('profit_loss_percent', 'misc'), ('binary_to_hex', 'computer_science'), ('multiply_complex_numbers', 'algebra'), ('geometric_progression', 'misc'), ('geometric_mean', 'misc'), ('harmonic_mean', 'misc'), ('euclidian_norm', 'misc'), ('angle_btw_vectors', 'geometry'), ('absolute_difference', 'basic_math'), ('vector_dot', 'algebra'), ('binary_2s_complement', 'computer_science'), ('invert_matrix', 'algebra'), ('sector_area', 'geometry'), ('mean_median', 'statistics'), ('int_matrix_22_determinant', 'algebra'), ('compound_interest', 'algebra'), ('decimal_to_hexadeci', 'computer_science'), ('percentage', 'basic_math'), ('celsius_to_fahrenheit', 'misc'), ('arithmetic_progression_term', 'misc'), ('arithmetic_progression_sum', 'misc'), ('decimal_to_octal', 'computer_science'), ('decimal_to_roman_numerals', 'misc'), ('degree_to_rad', 'geometry'), ('radian_to_deg', 'geometry'), ('trig_differentiation', 'calculus'), ('definite_integral', 'calculus'), ('is_prime', 'basic_math'), ('bcd_to_decimal', 'computer_science'), ('complex_to_polar', 'misc'), ('set_operation', 'misc'), ('base_conversion', 'misc'), ('curved_surface_area_cylinder', 'geometry'), ('perimeter_of_polygons', 'geometry'), ('power_of_powers', 'basic_math'), ('quotient_of_power_same_base', 'misc'), ('quotient_of_power_same_power', 'misc'), ('complex_quadratic', 'algebra'), ('is_leap_year', 'misc'), ('minutes_to_hours', 'misc'), ('decimal_to_bcd', 'computer_science'), ('circumference', 'geometry'), ('combine_like_terms', 'algebra'), ('signum_function', 'misc'), ('conditional_probability', 'statistics'), ('arc_length', 'geometry'), ('binomial_distribution', 'misc'), ('stationary_points', 'calculus'), ('expanding', 'algebra'), ('area_of_circle', 'geometry'), ('volume_cone_frustum', 'geometry'), ('equation_of_line_from_two_points', 'geometry'), ('area_of_circle_given_center_and_point', 'geometry'), ('factors', 'misc'), ('volume_hemisphere', 'geometry'), ('percentage_difference', 'basic_math'), ('percentage_error', 'basic_math'), ('greatest_common_divisor', 'basic_math'), ('product_of_scientific_notations', 'misc'), ('volume_pyramid', 'geometry'), ('surface_area_pyramid', 'geometry'), ('is_composite', 'basic_math'), ('complementary_and_supplementary_angle', 'geometry'), ('simplify_square_root', 'basic_math'), ('line_equation_from_2_points', 'algebra'), ('orthogonal_projection', 'algebra'), ('area_of_trapezoid', 'geometry'), ('tribonacci_series', 'computer_science'), ('nth_tribonacci_number', 'computer_science'), ('velocity_of_object', 'misc'), ('binary_addition', 'computer_science'), ('kinetic_energy', 'physics'), ('potential_dividers', 'physics'), ('resistivity', 'physics'), ('fringe_spacing', 'physics')]
diff --git a/docs/mathgenerator/physics.html b/docs/mathgenerator/physics.html index cc6e260..30d100c 100644 --- a/docs/mathgenerator/physics.html +++ b/docs/mathgenerator/physics.html @@ -61,6 +61,9 @@
  • resistivity
    • +
  • + fringe_spacing +
    • @@ -85,65 +88,85 @@ 
     1import random
  2import math
  3
- 4def kinetic_energy(max_mass=1000, max_vel=100):
- 5   r"""Kinetic Energy calculation using Ek = 0.5 * m * v^2
- 6
- 7    | Ex. Problem | Ex. Solution |
- 8    | --- | --- |
- 9    | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |
-10    """
-11   velocity = round(random.uniform(1, max_vel),2)
-12   mass = round(random.uniform(1, max_mass),2)
-13   kinetic_energy = round((0.5 * mass * velocity**2), 2)
-14
+ 4# Generic
+ 5def kinetic_energy(max_mass=1000, max_vel=100):
+ 6   r"""Kinetic Energy calculation using Ek = 0.5 * m * v^2
+ 7
+ 8    | Ex. Problem | Ex. Solution |
+ 9    | --- | --- |
+10    | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |
+11    """
+12   velocity = round(random.uniform(1, max_vel),2)
+13   mass = round(random.uniform(1, max_mass),2)
+14   kinetic_energy = round((0.5 * mass * velocity**2), 2)
 15
-16   problem = f"What is the kinetic energy of an object of mass ${mass} kg$ and velocity ${velocity} m/s$?"
-17   solution = f'${kinetic_energy} J$'
-18   return problem, solution
-19
-20def potential_dividers(max_vin=50, max_resistance=500):
-21   r"""Potential Divider question using Vout = (Vin * R2) / (R2 + R1)
-22
-23    | Ex. Problem | Ex. Solution |
-24    | --- | --- |
-25    | In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |
-26    """
-27   '''
-28    This is what a potential divider circuit looks like:
-29    ------
-30    |    R1
-31 Vi =    |----o
-32    |    R2      Vout
-33    |____|____o
-34    '''
-35   vin = random.randint(0, max_vin)          # Voltage input of cell
-36   r1 = random.randint(0, max_resistance)    # Resistance of R1
-37   r2 = random.randint(0, max_resistance)    # Resistance of R2
-38   vout = round((vin * r2) / (r1 + r2),2)    # Voltage output across R2
-39
-40   problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} Ω$ and ${r2} Ω$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?"
-41   solution = f"${vout} V$"
-42   return problem, solution
-43
-44def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):
-45   r"""Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire
+16
+17   problem = f"What is the kinetic energy of an object of mass ${mass} kg$ and velocity ${velocity} m/s$?"
+18   solution = f'${kinetic_energy} J$'
+19   return problem, solution
+20
+21
+22# Electricity
+23def potential_dividers(max_vin=50, max_resistance=500):
+24   r"""Potential Divider question using Vout = (Vin * R2) / (R2 + R1)
+25
+26    | Ex. Problem | Ex. Solution |
+27    | --- | --- |
+28    | In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |
+29    """
+30   '''
+31    This is what a potential divider circuit looks like:
+32    ------
+33    |    R1
+34 Vi =    |----o
+35    |    R2      Vout
+36    |____|____o
+37    '''
+38   vin = random.randint(0, max_vin)          # Voltage input of cell
+39   r1 = random.randint(0, max_resistance)    # Resistance of R1
+40   r2 = random.randint(0, max_resistance)    # Resistance of R2
+41   vout = round((vin * r2) / (r1 + r2),2)    # Voltage output across R2
+42
+43   problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} \\Omega$ and ${r2} \\Omega$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?"
+44   solution = f"${vout} V$"
+45   return problem, solution
 46
-47    | Ex. Problem | Ex. Solution |
-48    | --- | --- |
-49    | A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 Ωm$ |
-50    """
-51   # This question requires a lot of unit conversions and calculating the area of a circle from diameter
-52   diameter_mm = round(random.uniform(0, max_diameter_mm),2)   # Random diameter in mm
-53   cross_sectional_area = math.pi * (diameter_mm / 2000)**2    # Calculate the cross sectional area using pi r²
-54   length_cm = round(random.uniform(0, max_length_cm),2)       # Random wire length in cm
-55   resistance = round(random.uniform(0, max_resistance),2)     # Random reistance in ohms
-56
-57   resistivity = (resistance * cross_sectional_area) / (length_cm / 100)
-58
-59   problem = f"A wire has resistance ${resistance*1000} mΩ$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire"
-60   solution = f"${resistivity:.2e} Ωm$"
+47def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):
+48   r"""Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire
+49
+50    | Ex. Problem | Ex. Solution |
+51    | --- | --- |
+52    | A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 \Omega m$ |
+53    """
+54   # This question requires a lot of unit conversions and calculating the area of a circle from diameter
+55   diameter_mm = round(random.uniform(0, max_diameter_mm),2)   # Random diameter in mm
+56   cross_sectional_area = math.pi * (diameter_mm / 2000)**2    # Calculate the cross sectional area using pi r²
+57   length_cm = round(random.uniform(0, max_length_cm),2)       # Random wire length in cm
+58   resistance = round(random.uniform(0, max_resistance),2)     # Random reistance in ohms
+59
+60   resistivity = (resistance * cross_sectional_area) / (length_cm / 100)
 61
-62   return problem, solution
+62   problem = f"A wire has resistance ${resistance*1000} m\\Omega$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire"
+63   solution = f"${resistivity:.2e} \\Omega m$"
+64
+65   return problem, solution
+66
+67# Waves
+68def fringe_spacing(max_screen_distance=30, max_slit_spacing_mm=100):
+69   r"""Calculate the fringe spacing in a double slit experiment with w=(λD)/s
+70    | Ex. Problem | Ex. Solution |
+71    | --- | --- |
+72    | A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen.  The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes. | Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$ |
+73    """
+74   wavelength_nm = random.randint(380,750)      # Random wavelength between violet and red (nm)
+75   screen_distance = random.randint(0, max_screen_distance)    # Random distance between screen and slits (m)
+76   slit_spacing_mm = random.randint(0, max_slit_spacing_mm)    # Random slit spacing (mm)
+77
+78   fringe_spacing = round((((wavelength_nm * 10**-9) * screen_distance) / (slit_spacing_mm * 10**-3)),5)
+79
+80   problem = f"A laser with a wavelength of ${wavelength_nm}nm$ is shone through a double slit system to produce an interference pattern on a screen.  The screen is ${screen_distance}m$ from the slits and the slits are ${slit_spacing_mm}mm$ apart. Calculate the spacing between the bright fringes."
+81   solution = f"Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of ${fringe_spacing}m$"
+82   return problem, solution
    @@ -159,21 +182,21 @@ - 
     5def kinetic_energy(max_mass=1000, max_vel=100):
- 6   r"""Kinetic Energy calculation using Ek = 0.5 * m * v^2
- 7
- 8    | Ex. Problem | Ex. Solution |
- 9    | --- | --- |
-10    | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |
-11    """
-12   velocity = round(random.uniform(1, max_vel),2)
-13   mass = round(random.uniform(1, max_mass),2)
-14   kinetic_energy = round((0.5 * mass * velocity**2), 2)
-15
+            
     6def kinetic_energy(max_mass=1000, max_vel=100):
+ 7   r"""Kinetic Energy calculation using Ek = 0.5 * m * v^2
+ 8
+ 9    | Ex. Problem | Ex. Solution |
+10    | --- | --- |
+11    | What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$ | $250 J$ |
+12    """
+13   velocity = round(random.uniform(1, max_vel),2)
+14   mass = round(random.uniform(1, max_mass),2)
+15   kinetic_energy = round((0.5 * mass * velocity**2), 2)
 16
-17   problem = f"What is the kinetic energy of an object of mass ${mass} kg$ and velocity ${velocity} m/s$?"
-18   solution = f'${kinetic_energy} J$'
-19   return problem, solution
+17
+18   problem = f"What is the kinetic energy of an object of mass ${mass} kg$ and velocity ${velocity} m/s$?"
+19   solution = f'${kinetic_energy} J$'
+20   return problem, solution
 
    
 
 
@@ -208,29 +231,29 @@
    - 
    21def potential_dividers(max_vin=50, max_resistance=500):
-22   r"""Potential Divider question using Vout = (Vin * R2) / (R2 + R1)
-23
-24    | Ex. Problem | Ex. Solution |
-25    | --- | --- |
-26    | In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |
-27    """
-28   '''
-29    This is what a potential divider circuit looks like:
-30    ------
-31    |    R1
-32 Vi =    |----o
-33    |    R2      Vout
-34    |____|____o
-35    '''
-36   vin = random.randint(0, max_vin)          # Voltage input of cell
-37   r1 = random.randint(0, max_resistance)    # Resistance of R1
-38   r2 = random.randint(0, max_resistance)    # Resistance of R2
-39   vout = round((vin * r2) / (r1 + r2),2)    # Voltage output across R2
-40
-41   problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} Ω$ and ${r2} Ω$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?"
-42   solution = f"${vout} V$"
-43   return problem, solution
+            
    24def potential_dividers(max_vin=50, max_resistance=500):
+25   r"""Potential Divider question using Vout = (Vin * R2) / (R2 + R1)
+26
+27    | Ex. Problem | Ex. Solution |
+28    | --- | --- |
+29    | In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ |
+30    """
+31   '''
+32    This is what a potential divider circuit looks like:
+33    ------
+34    |    R1
+35 Vi =    |----o
+36    |    R2      Vout
+37    |____|____o
+38    '''
+39   vin = random.randint(0, max_vin)          # Voltage input of cell
+40   r1 = random.randint(0, max_resistance)    # Resistance of R1
+41   r2 = random.randint(0, max_resistance)    # Resistance of R2
+42   vout = round((vin * r2) / (r1 + r2),2)    # Voltage output across R2
+43
+44   problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} \\Omega$ and ${r2} \\Omega$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?"
+45   solution = f"${vout} V$"
+46   return problem, solution
 
    
 
 
@@ -245,7 +268,7 @@
 
 
 
-  In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2?
+  In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2?
   $4 V$
 
 
@@ -265,25 +288,25 @@
    - 
    45def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):
-46   r"""Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire
-47
-48    | Ex. Problem | Ex. Solution |
-49    | --- | --- |
-50    | A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 Ωm$ |
-51    """
-52   # This question requires a lot of unit conversions and calculating the area of a circle from diameter
-53   diameter_mm = round(random.uniform(0, max_diameter_mm),2)   # Random diameter in mm
-54   cross_sectional_area = math.pi * (diameter_mm / 2000)**2    # Calculate the cross sectional area using pi r²
-55   length_cm = round(random.uniform(0, max_length_cm),2)       # Random wire length in cm
-56   resistance = round(random.uniform(0, max_resistance),2)     # Random reistance in ohms
-57
-58   resistivity = (resistance * cross_sectional_area) / (length_cm / 100)
-59
-60   problem = f"A wire has resistance ${resistance*1000} mΩ$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire"
-61   solution = f"${resistivity:.2e} Ωm$"
+            
    48def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):
+49   r"""Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire
+50
+51    | Ex. Problem | Ex. Solution |
+52    | --- | --- |
+53    | A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 \Omega m$ |
+54    """
+55   # This question requires a lot of unit conversions and calculating the area of a circle from diameter
+56   diameter_mm = round(random.uniform(0, max_diameter_mm),2)   # Random diameter in mm
+57   cross_sectional_area = math.pi * (diameter_mm / 2000)**2    # Calculate the cross sectional area using pi r²
+58   length_cm = round(random.uniform(0, max_length_cm),2)       # Random wire length in cm
+59   resistance = round(random.uniform(0, max_resistance),2)     # Random reistance in ohms
+60
+61   resistivity = (resistance * cross_sectional_area) / (length_cm / 100)
 62
-63   return problem, solution
+63   problem = f"A wire has resistance ${resistance*1000} m\\Omega$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire"
+64   solution = f"${resistivity:.2e} \\Omega m$"
+65
+66   return problem, solution
 
    
 
 
@@ -298,8 +321,57 @@
 
 
 
-  A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire
-  $6.14e-07 Ωm$
+  A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire
+  $6.14e-07 \Omega m$
+
+
+
+
    + + + +
    + +
    + + def + fringe_spacing(max_screen_distance=30, max_slit_spacing_mm=100): + + + +
    + + 
    69def fringe_spacing(max_screen_distance=30, max_slit_spacing_mm=100):
+70   r"""Calculate the fringe spacing in a double slit experiment with w=(λD)/s
+71    | Ex. Problem | Ex. Solution |
+72    | --- | --- |
+73    | A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen.  The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes. | Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$ |
+74    """
+75   wavelength_nm = random.randint(380,750)      # Random wavelength between violet and red (nm)
+76   screen_distance = random.randint(0, max_screen_distance)    # Random distance between screen and slits (m)
+77   slit_spacing_mm = random.randint(0, max_slit_spacing_mm)    # Random slit spacing (mm)
+78
+79   fringe_spacing = round((((wavelength_nm * 10**-9) * screen_distance) / (slit_spacing_mm * 10**-3)),5)
+80
+81   problem = f"A laser with a wavelength of ${wavelength_nm}nm$ is shone through a double slit system to produce an interference pattern on a screen.  The screen is ${screen_distance}m$ from the slits and the slits are ${slit_spacing_mm}mm$ apart. Calculate the spacing between the bright fringes."
+82   solution = f"Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of ${fringe_spacing}m$"
+83   return problem, solution
+
    + + +

    Calculate the fringe spacing in a double slit experiment with w=(λD)/s

    + + + + + + + + + + + +
    Ex. ProblemEx. Solution
    A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes.Using the equation $\frac{{\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$
    diff --git a/docs/search.js b/docs/search.js index 6d23efb..a45d4d9 100644 --- a/docs/search.js +++ b/docs/search.js @@ -1,6 +1,6 @@ window.pdocSearch = (function(){ /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();omathgenerator\n\n

    Fork of https://github.com/lukew3/mathgenerator
    \nAdding more Physics and Computer Science questions

    \n\n

    A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.

    \n\n

    To try out generators, go to https://mathgenerator-demo.netlify.app

    \n\n

    See CONTRIBUTING.md for information about how to contribute.

    \n\n

    Table of Contents

    \n\n\n\n

    Installation

    \n\n

    The project can be install via pip

    \n\n
    \n
    pip install mathgenerator\n
    \n
    \n\n

    Usage

    \n\n

    Here is an example of how you would generate an addition problem:

    \n\n
    \n
    import mathgenerator\n\n#generate an addition problem\nproblem, solution = mathgenerator.addition()\n\n#another way to generate an addition problem using genById()\nproblem, solution = mathgenerator.genById(0)\n
    \n
    \n\n

    You may prefer to use import mathgenerator as mg and run functions like mg.addition() so that you don't have to type as much.\n\nProblem/solution pairs are generated with either:

    \n\n
      \n
    • mathgenerator.<generator_name>() - generates a problem, solution set from the given generator name.
      • \n
    • mathgenerator.genById(id) - generates a problem, solution set with generator id provided by the id parameter
      • \n
    \n\n

    \nYou can also use getGenList() to return a list of all generators included in the library in the format:\n\n\n

    [funcname, subjectname]\n
    \n\n

    Documentation

    \n\n

    Documentation can be found at https://lukew3.github.io/mathgenerator

    \n"}, "mathgenerator.get_gen_list": {"fullname": "mathgenerator.get_gen_list", "modulename": "mathgenerator", "qualname": "get_gen_list", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.gen_by_id": {"fullname": "mathgenerator.gen_by_id", "modulename": "mathgenerator", "qualname": "gen_by_id", "kind": "function", "doc": "

    \n", "signature": "(id, *args, **kwargs):", "funcdef": "def"}, "mathgenerator.getGenList": {"fullname": "mathgenerator.getGenList", "modulename": "mathgenerator", "qualname": "getGenList", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.genById": {"fullname": "mathgenerator.genById", "modulename": "mathgenerator", "qualname": "genById", "kind": "function", "doc": "

    \n", "signature": "(id, *args, **kwargs):", "funcdef": "def"}, "mathgenerator.algebra": {"fullname": "mathgenerator.algebra", "modulename": "mathgenerator.algebra", "kind": "module", "doc": "

    \n"}, "mathgenerator.algebra.basic_algebra": {"fullname": "mathgenerator.algebra.basic_algebra", "modulename": "mathgenerator.algebra", "qualname": "basic_algebra", "kind": "function", "doc": "

    Basic Algebra

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $1x + 5 = 5$$0$
    \n", "signature": "(max_variable=10):", "funcdef": "def"}, "mathgenerator.algebra.combine_like_terms": {"fullname": "mathgenerator.algebra.combine_like_terms", "modulename": "mathgenerator.algebra", "qualname": "combine_like_terms", "kind": "function", "doc": "

    Combine Like Terms

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $6x^{9} + 3x^{2} + 5x^{19} + 3x^{17}$$3x^{2} + 6x^{9} + 3x^{17} + 5x^{19}$
    \n", "signature": "(max_coef=10, max_exp=20, max_terms=10):", "funcdef": "def"}, "mathgenerator.algebra.complex_quadratic": {"fullname": "mathgenerator.algebra.complex_quadratic", "modulename": "mathgenerator.algebra", "qualname": "complex_quadratic", "kind": "function", "doc": "

    Complex Quadratic Equation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$$((-1.172, -6.828)) = (\\frac{-8 + \\sqrt{32}}{2}, (\\frac{-8 - \\sqrt{32}}{2})$
    \n", "signature": "(prob_type=0, max_range=10):", "funcdef": "def"}, "mathgenerator.algebra.compound_interest": {"fullname": "mathgenerator.algebra.compound_interest", "modulename": "mathgenerator.algebra", "qualname": "compound_interest", "kind": "function", "doc": "

    Compound Interest

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Compound interest for a principle amount of $2679$ dollars, $9$% rate of interest and for a time period of $3$ years is $=$$3469.38$
    \n", "signature": "(max_principle=10000, max_rate=10, max_time=10):", "funcdef": "def"}, "mathgenerator.algebra.distance_two_points": {"fullname": "mathgenerator.algebra.distance_two_points", "modulename": "mathgenerator.algebra", "qualname": "distance_two_points", "kind": "function", "doc": "

    Distance between 2 points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the distance between $(-19, -6)$ and $(15, -16)$$\\sqrt{1256}$
    \n", "signature": "(max_val_xy=20, min_val_xy=-20):", "funcdef": "def"}, "mathgenerator.algebra.expanding": {"fullname": "mathgenerator.algebra.expanding", "modulename": "mathgenerator.algebra", "qualname": "expanding", "kind": "function", "doc": "

    Expanding Factored Binomial

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $(x-6)(-3x-3)$$x^2+18x+18$
    \n", "signature": "(range_x1=10, range_x2=10, range_a=10, range_b=10):", "funcdef": "def"}, "mathgenerator.algebra.factoring": {"fullname": "mathgenerator.algebra.factoring", "modulename": "mathgenerator.algebra", "qualname": "factoring", "kind": "function", "doc": "

    Factoring Quadratic\nGiven a quadratic equation in the form x^2 + bx + c, factor it into it's roots (x - x1)(x -x2)

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $x^2+2x-24$$(x-4)(x+6)$
    \n", "signature": "(range_x1=10, range_x2=10):", "funcdef": "def"}, "mathgenerator.algebra.int_matrix_22_determinant": {"fullname": "mathgenerator.algebra.int_matrix_22_determinant", "modulename": "mathgenerator.algebra", "qualname": "int_matrix_22_determinant", "kind": "function", "doc": "

    Determinant to 2x2 Matrix

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\det \\begin{bmatrix} 88 & 40 \\\\ 9 & 91 \\end{bmatrix}= $$7648$
    \n", "signature": "(max_matrix_val=100):", "funcdef": "def"}, "mathgenerator.algebra.intersection_of_two_lines": {"fullname": "mathgenerator.algebra.intersection_of_two_lines", "modulename": "mathgenerator.algebra", "qualname": "intersection_of_two_lines", "kind": "function", "doc": "

    Intersection of two lines

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the point of intersection of the two lines: $y = \\frac{-2}{6}x + 3$ and $y = \\frac{3}{6}x - 8$$(\\frac{66}{5}, \\frac{-7}{5})$
    \n", "signature": "(\tmin_m=-10,\tmax_m=10,\tmin_b=-10,\tmax_b=10,\tmin_denominator=1,\tmax_denominator=6):", "funcdef": "def"}, "mathgenerator.algebra.invert_matrix": {"fullname": "mathgenerator.algebra.invert_matrix", "modulename": "mathgenerator.algebra", "qualname": "invert_matrix", "kind": "function", "doc": "

    Invert Matrix

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Inverse of Matrix $\\begin{bmatrix} 4 & 1 & 4 \\\\ 5 & 1 & 5 \\\\ 12 & 3 & 13 \\end{bmatrix}$ is:$\\begin{bmatrix} 2 & 1 & -1 \\\\ 5 & -4 & 0 \\\\ -3 & 0 & 1 \\end{bmatrix}$
    \n", "signature": "(\tsquare_matrix_dimension=3,\tmax_matrix_element=99,\tonly_integer_elements_in_inverted_matrixe=True):", "funcdef": "def"}, "mathgenerator.algebra.linear_equations": {"fullname": "mathgenerator.algebra.linear_equations", "modulename": "mathgenerator.algebra", "qualname": "linear_equations", "kind": "function", "doc": "

    Linear Equations

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given the equations $10x + -20y = 310$ and $-16x + -17y = 141$, solve for $x$ and $y$$x = 5$, $y = -13$
    \n", "signature": "(n=2, var_range=20, coeff_range=20):", "funcdef": "def"}, "mathgenerator.algebra.line_equation_from_2_points": {"fullname": "mathgenerator.algebra.line_equation_from_2_points", "modulename": "mathgenerator.algebra", "qualname": "line_equation_from_2_points", "kind": "function", "doc": "

    Equation of Line from Two Points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the equation of the line passing through the points $(-19,-8)$ and $(-2,0)$.$y=\\frac{8}{17}x+\\frac{16}{17}$
    \n", "signature": "(max_val=20):", "funcdef": "def"}, "mathgenerator.algebra.log": {"fullname": "mathgenerator.algebra.log", "modulename": "mathgenerator.algebra", "qualname": "log", "kind": "function", "doc": "

    Logarithm

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $log_{3}(243)=$$5$
    \n", "signature": "(max_base=3, max_val=8):", "funcdef": "def"}, "mathgenerator.algebra.matrix_multiplication": {"fullname": "mathgenerator.algebra.matrix_multiplication", "modulename": "mathgenerator.algebra", "qualname": "matrix_multiplication", "kind": "function", "doc": "

    Multiply Two Matrices

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Multiply $\\begin{bmatrix} 15 & 72 \\\\ 64 & -20 \\\\ 18 & 59 \\\\ -21 & -55 \\\\ 20 & -12 \\\\ -75 & -42 \\\\ 47 & 89 \\\\ -53 & 27 \\\\ -56 & 44 \\end{bmatrix}$ and $\\begin{bmatrix} 49 & -2 & 68 & -28 \\\\ 49 & 6 & 83 & 42 \\end{bmatrix}$$\\begin{bmatrix} 4263 & 402 & 6996 & 2604 \\\\ 2156 & -248 & 2692 & -2632 \\\\ 3773 & 318 & 6121 & 1974 \\\\ -3724 & -288 & -5993 & -1722 \\\\ 392 & -112 & 364 & -1064 \\\\ -5733 & -102 & -8586 & 336 \\\\ 6664 & 440 & 10583 & 2422 \\\\ -1274 & 268 & -1363 & 2618 \\\\ -588 & 376 & -156 & 3416 \\end{bmatrix}$
    \n", "signature": "(max_val=100, max_dim=10):", "funcdef": "def"}, "mathgenerator.algebra.midpoint_of_two_points": {"fullname": "mathgenerator.algebra.midpoint_of_two_points", "modulename": "mathgenerator.algebra", "qualname": "midpoint_of_two_points", "kind": "function", "doc": "

    Midpoint of two points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The midpoint of $(-8,10)$ and $(18,0) = $$(5.0,5.0)$
    \n", "signature": "(max_value=20):", "funcdef": "def"}, "mathgenerator.algebra.multiply_complex_numbers": {"fullname": "mathgenerator.algebra.multiply_complex_numbers", "modulename": "mathgenerator.algebra", "qualname": "multiply_complex_numbers", "kind": "function", "doc": "

    Multiplication of 2 complex numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $(14+18j) * (14+15j) = $$(-74+462j)$
    \n", "signature": "(min_real_imaginary_num=-20, max_real_imaginary_num=20):", "funcdef": "def"}, "mathgenerator.algebra.multiply_int_to_22_matrix": {"fullname": "mathgenerator.algebra.multiply_int_to_22_matrix", "modulename": "mathgenerator.algebra", "qualname": "multiply_int_to_22_matrix", "kind": "function", "doc": "

    Multiply Integer to 2x2 Matrix

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $5 * \\begin{bmatrix} 1 & 0 \\\\ 2 & 9 \\end{bmatrix} =$$\\begin{bmatrix} 5 & 0 \\\\ 10 & 45 \\end{bmatrix}$
    \n", "signature": "(max_matrix_val=10, max_res=100):", "funcdef": "def"}, "mathgenerator.algebra.quadratic_equation": {"fullname": "mathgenerator.algebra.quadratic_equation", "modulename": "mathgenerator.algebra", "qualname": "quadratic_equation", "kind": "function", "doc": "

    Quadratic Equation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What are the zeros of the quadratic equation $22x^2+137x+25=0$${-0.19, -6.04}$
    \n", "signature": "(max_val=100):", "funcdef": "def"}, "mathgenerator.algebra.simple_interest": {"fullname": "mathgenerator.algebra.simple_interest", "modulename": "mathgenerator.algebra", "qualname": "simple_interest", "kind": "function", "doc": "

    Simple Interest

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Simple interest for a principle amount of $7217$ dollars, $3$% rate of interest and for a time period of $10$ years is $=$$2165.1$
    \n", "signature": "(max_principle=10000, max_rate=10, max_time=10):", "funcdef": "def"}, "mathgenerator.algebra.system_of_equations": {"fullname": "mathgenerator.algebra.system_of_equations", "modulename": "mathgenerator.algebra", "qualname": "system_of_equations", "kind": "function", "doc": "

    Solve a System of Equations in R^2

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given $-x + 5y = -28$ and $9x + 2y = 64$, solve for $x$ and $y$.$x = 8$, $y = -4$
    \n", "signature": "(range_x=10, range_y=10, coeff_mult_range=10):", "funcdef": "def"}, "mathgenerator.algebra.vector_cross": {"fullname": "mathgenerator.algebra.vector_cross", "modulename": "mathgenerator.algebra", "qualname": "vector_cross", "kind": "function", "doc": "

    Cross product of 2 vectors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $[-1, -4, 10] \\times [-11, 1, -16] = $$[54, -126, -45]$
    \n", "signature": "(min_val=-20, max_val=20):", "funcdef": "def"}, "mathgenerator.algebra.vector_dot": {"fullname": "mathgenerator.algebra.vector_dot", "modulename": "mathgenerator.algebra", "qualname": "vector_dot", "kind": "function", "doc": "

    Dot product of 2 vectors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $[12, -9, -8]\\cdot[-9, 8, 1]=$$-188$
    \n", "signature": "(min_val=-20, max_val=20):", "funcdef": "def"}, "mathgenerator.algebra.orthogonal_projection": {"fullname": "mathgenerator.algebra.orthogonal_projection", "modulename": "mathgenerator.algebra", "qualname": "orthogonal_projection", "kind": "function", "doc": "

    Orthogonal Projection

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the orthogonal projection of $[2, 3]$ onto $[4, -7]$$[\\frac{-4}{5}, \\frac{7}{5}]$
    \n", "signature": "(min_val=-10, max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math": {"fullname": "mathgenerator.basic_math", "modulename": "mathgenerator.basic_math", "kind": "module", "doc": "

    \n"}, "mathgenerator.basic_math.absolute_difference": {"fullname": "mathgenerator.basic_math.absolute_difference", "modulename": "mathgenerator.basic_math", "qualname": "absolute_difference", "kind": "function", "doc": "

    Absolute difference between two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $|22-34|=$$12$
    \n", "signature": "(max_a=100, max_b=100):", "funcdef": "def"}, "mathgenerator.basic_math.addition": {"fullname": "mathgenerator.basic_math.addition", "modulename": "mathgenerator.basic_math", "qualname": "addition", "kind": "function", "doc": "

    Addition of two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $22+34=$$56$
    \n", "signature": "(max_sum=99, max_addend=50):", "funcdef": "def"}, "mathgenerator.basic_math.compare_fractions": {"fullname": "mathgenerator.basic_math.compare_fractions", "modulename": "mathgenerator.basic_math", "qualname": "compare_fractions", "kind": "function", "doc": "

    Compare Fractions

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Which symbol represents the comparison between $\\frac{1}{2}$ and $\\frac{3}{4}$?$>$
    \n", "signature": "(max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math.cube_root": {"fullname": "mathgenerator.basic_math.cube_root", "modulename": "mathgenerator.basic_math", "qualname": "cube_root", "kind": "function", "doc": "

    Cube Root

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the cube root of: $\\sqrt[3]{125}=$ to 2 decimal places?$5$
    \n", "signature": "(min_no=1, max_no=1000):", "funcdef": "def"}, "mathgenerator.basic_math.divide_fractions": {"fullname": "mathgenerator.basic_math.divide_fractions", "modulename": "mathgenerator.basic_math", "qualname": "divide_fractions", "kind": "function", "doc": "

    Divide Fractions

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\frac{7}{9}\\div\\frac{4}{1}=$$\\frac{7}{36}$
    \n", "signature": "(max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math.division": {"fullname": "mathgenerator.basic_math.division", "modulename": "mathgenerator.basic_math", "qualname": "division", "kind": "function", "doc": "

    Division

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $216\\div24=$$9$
    \n", "signature": "(max_a=25, max_b=25):", "funcdef": "def"}, "mathgenerator.basic_math.exponentiation": {"fullname": "mathgenerator.basic_math.exponentiation", "modulename": "mathgenerator.basic_math", "qualname": "exponentiation", "kind": "function", "doc": "

    Exponentiation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $9^{5}=$$8$
    \n", "signature": "(max_base=20, max_expo=10):", "funcdef": "def"}, "mathgenerator.basic_math.factorial": {"fullname": "mathgenerator.basic_math.factorial", "modulename": "mathgenerator.basic_math", "qualname": "factorial", "kind": "function", "doc": "

    Factorial

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $4! =$$24$
    \n", "signature": "(max_input=6):", "funcdef": "def"}, "mathgenerator.basic_math.fraction_multiplication": {"fullname": "mathgenerator.basic_math.fraction_multiplication", "modulename": "mathgenerator.basic_math", "qualname": "fraction_multiplication", "kind": "function", "doc": "

    Fraction Multiplication

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\frac{3}{10}\\cdot\\frac{6}{7}=$$\\frac{9}{35}$
    \n", "signature": "(max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math.fraction_to_decimal": {"fullname": "mathgenerator.basic_math.fraction_to_decimal", "modulename": "mathgenerator.basic_math", "qualname": "fraction_to_decimal", "kind": "function", "doc": "

    Fraction to Decimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $83\\div80=$$1.04$
    \n", "signature": "(max_res=99, max_divid=99):", "funcdef": "def"}, "mathgenerator.basic_math.greatest_common_divisor": {"fullname": "mathgenerator.basic_math.greatest_common_divisor", "modulename": "mathgenerator.basic_math", "qualname": "greatest_common_divisor", "kind": "function", "doc": "

    Greatest Common Divisor of N Numbers ( GCD / HCF )

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $GCD(488075608, 75348096)=$$8$
    \n", "signature": "(numbers_count=2, max_num=1000):", "funcdef": "def"}, "mathgenerator.basic_math.is_composite": {"fullname": "mathgenerator.basic_math.is_composite", "modulename": "mathgenerator.basic_math", "qualname": "is_composite", "kind": "function", "doc": "

    Is Composite

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Is $171$ composite?Yes
    \n", "signature": "(max_num=250):", "funcdef": "def"}, "mathgenerator.basic_math.is_prime": {"fullname": "mathgenerator.basic_math.is_prime", "modulename": "mathgenerator.basic_math", "qualname": "is_prime", "kind": "function", "doc": "

    Is Prime

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Is $37$ prime?Yes
    \n", "signature": "(max_num=100):", "funcdef": "def"}, "mathgenerator.basic_math.multiplication": {"fullname": "mathgenerator.basic_math.multiplication", "modulename": "mathgenerator.basic_math", "qualname": "multiplication", "kind": "function", "doc": "

    Multiplication

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $10\\cdot9=$$90$
    \n", "signature": "(max_multi=12):", "funcdef": "def"}, "mathgenerator.basic_math.percentage": {"fullname": "mathgenerator.basic_math.percentage", "modulename": "mathgenerator.basic_math", "qualname": "percentage", "kind": "function", "doc": "

    Percentage of a number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is $45$% of $39$?$17.55$
    \n", "signature": "(max_value=99, max_percentage=99):", "funcdef": "def"}, "mathgenerator.basic_math.percentage_difference": {"fullname": "mathgenerator.basic_math.percentage_difference", "modulename": "mathgenerator.basic_math", "qualname": "percentage_difference", "kind": "function", "doc": "

    Percentage difference between two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the percentage difference between $2$ and $10$?$133.33$
    \n", "signature": "(max_value=200, min_value=0):", "funcdef": "def"}, "mathgenerator.basic_math.percentage_error": {"fullname": "mathgenerator.basic_math.percentage_error", "modulename": "mathgenerator.basic_math", "qualname": "percentage_error", "kind": "function", "doc": "

    Percentage error

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the percentage error when observed value equals $32$ and exact value equals $81$.$60.49$%
    \n", "signature": "(max_value=100, min_value=-100):", "funcdef": "def"}, "mathgenerator.basic_math.power_of_powers": {"fullname": "mathgenerator.basic_math.power_of_powers", "modulename": "mathgenerator.basic_math", "qualname": "power_of_powers", "kind": "function", "doc": "

    Power of Powers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Simplify $18^{10^{8}}$$18^{80}$
    \n", "signature": "(max_base=50, max_power=10):", "funcdef": "def"}, "mathgenerator.basic_math.square": {"fullname": "mathgenerator.basic_math.square", "modulename": "mathgenerator.basic_math", "qualname": "square", "kind": "function", "doc": "

    Square

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $17^2=$$289$
    \n", "signature": "(max_square_num=20):", "funcdef": "def"}, "mathgenerator.basic_math.square_root": {"fullname": "mathgenerator.basic_math.square_root", "modulename": "mathgenerator.basic_math", "qualname": "square_root", "kind": "function", "doc": "

    Square Root

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\sqrt{64}=$$8$
    \n", "signature": "(min_no=1, max_no=12):", "funcdef": "def"}, "mathgenerator.basic_math.simplify_square_root": {"fullname": "mathgenerator.basic_math.simplify_square_root", "modulename": "mathgenerator.basic_math", "qualname": "simplify_square_root", "kind": "function", "doc": "

    Simplify Square Root

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\sqrt{63}$$3\\sqrt{7}$
    \n", "signature": "(max_variable=100):", "funcdef": "def"}, "mathgenerator.basic_math.subtraction": {"fullname": "mathgenerator.basic_math.subtraction", "modulename": "mathgenerator.basic_math", "qualname": "subtraction", "kind": "function", "doc": "

    Subtraction of two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $54-22=$$32$
    \n", "signature": "(max_minuend=99, max_diff=99):", "funcdef": "def"}, "mathgenerator.calculus": {"fullname": "mathgenerator.calculus", "modulename": "mathgenerator.calculus", "kind": "module", "doc": "

    \n"}, "mathgenerator.calculus.definite_integral": {"fullname": "mathgenerator.calculus.definite_integral", "modulename": "mathgenerator.calculus", "qualname": "definite_integral", "kind": "function", "doc": "

    Definite Integral of Quadratic Equation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The definite integral within limits $0$ to $1$ of the equation $28x^2 + 32x + 66 = $$91.33$
    \n", "signature": "(max_coef=100):", "funcdef": "def"}, "mathgenerator.calculus.power_rule_differentiation": {"fullname": "mathgenerator.calculus.power_rule_differentiation", "modulename": "mathgenerator.calculus", "qualname": "power_rule_differentiation", "kind": "function", "doc": "

    Power Rule Differentiation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Differentiate $1x^{5} + 4x^{7} + 4x^{4}$$5x^{4} + 28x^{6} + 16x^{3}$
    \n", "signature": "(max_coef=10, max_exp=10, max_terms=5):", "funcdef": "def"}, "mathgenerator.calculus.power_rule_integration": {"fullname": "mathgenerator.calculus.power_rule_integration", "modulename": "mathgenerator.calculus", "qualname": "power_rule_integration", "kind": "function", "doc": "

    Power Rule Integration

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Integrate $9x^{6} + 2x^{6} + 4x^{3}$$\\frac{9}{6}x^{7} + \\frac{2}{6}x^{7} + \\frac{4}{3}x^{4} + C$
    \n", "signature": "(max_coef=10, max_exp=10, max_terms=5):", "funcdef": "def"}, "mathgenerator.calculus.stationary_points": {"fullname": "mathgenerator.calculus.stationary_points", "modulename": "mathgenerator.calculus", "qualname": "stationary_points", "kind": "function", "doc": "

    Stationary Points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $f(x)=6x^3 + 6x^2 + x + 8$${- \\frac{1}{3} - \\frac{\\sqrt{2}}{6}, - \\frac{1}{3} + \\frac{\\sqrt{2}}{6}}$
    \n", "signature": "(max_exp=3, max_coef=10):", "funcdef": "def"}, "mathgenerator.calculus.trig_differentiation": {"fullname": "mathgenerator.calculus.trig_differentiation", "modulename": "mathgenerator.calculus", "qualname": "trig_differentiation", "kind": "function", "doc": "

    Trigonometric Differentiation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\frac{d}{dx}(\\csc)=$$-\\csc \\cdot \\cot$
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.computer_science": {"fullname": "mathgenerator.computer_science", "modulename": "mathgenerator.computer_science", "kind": "module", "doc": "

    \n"}, "mathgenerator.computer_science.binary_addition": {"fullname": "mathgenerator.computer_science.binary_addition", "modulename": "mathgenerator.computer_science", "qualname": "binary_addition", "kind": "function", "doc": "

    Binary Addition

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    In binary, calculate: $101 + 110110 = $$111011$
    \n", "signature": "(max_sum=256, max_addend=128):", "funcdef": "def"}, "mathgenerator.computer_science.bcd_to_decimal": {"fullname": "mathgenerator.computer_science.bcd_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "bcd_to_decimal", "kind": "function", "doc": "

    Binary Coded Decimal to Integer

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Integer of Binary Coded Decimal $4 =$$17801$
    \n", "signature": "(max_number=10000):", "funcdef": "def"}, "mathgenerator.computer_science.binary_2s_complement": {"fullname": "mathgenerator.computer_science.binary_2s_complement", "modulename": "mathgenerator.computer_science", "qualname": "binary_2s_complement", "kind": "function", "doc": "

    Binary 2's Complement

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    2's complement of $1011 = $$101$
    \n", "signature": "(maxDigits=10):", "funcdef": "def"}, "mathgenerator.computer_science.binary_complement_1s": {"fullname": "mathgenerator.computer_science.binary_complement_1s", "modulename": "mathgenerator.computer_science", "qualname": "binary_complement_1s", "kind": "function", "doc": "

    Binary Complement 1s

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $1111001 = $$0000110$
    \n", "signature": "(maxDigits=10):", "funcdef": "def"}, "mathgenerator.computer_science.binary_to_decimal": {"fullname": "mathgenerator.computer_science.binary_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_decimal", "kind": "function", "doc": "

    Binary to Decimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $000110$$6$
    \n", "signature": "(max_dig=10):", "funcdef": "def"}, "mathgenerator.computer_science.binary_to_hex": {"fullname": "mathgenerator.computer_science.binary_to_hex", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_hex", "kind": "function", "doc": "

    Binary to Hexidecimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $010101$$0x15$
    \n", "signature": "(max_dig=10):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_bcd": {"fullname": "mathgenerator.computer_science.decimal_to_bcd", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_bcd", "kind": "function", "doc": "

    Decimal to Binary Coded Decimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    BCD of Decimal Number $6575 = $$191015$
    \n", "signature": "(max_number=10000):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_binary": {"fullname": "mathgenerator.computer_science.decimal_to_binary", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_binary", "kind": "function", "doc": "

    Decimal to Binary

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Binary of $4 = $$100$
    \n", "signature": "(max_dec=99):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_hexadeci": {"fullname": "mathgenerator.computer_science.decimal_to_hexadeci", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_hexadeci", "kind": "function", "doc": "

    Decimal to Hexadecimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Hexadecimal of $410 = $$0x19a$
    \n", "signature": "(max_dec=1000):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_octal": {"fullname": "mathgenerator.computer_science.decimal_to_octal", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_octal", "kind": "function", "doc": "

    Decimal to Octal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The decimal number $3698$ in octal is:$0o7162$
    \n", "signature": "(max_decimal=4096):", "funcdef": "def"}, "mathgenerator.computer_science.fibonacci_series": {"fullname": "mathgenerator.computer_science.fibonacci_series", "modulename": "mathgenerator.computer_science", "qualname": "fibonacci_series", "kind": "function", "doc": "

    Fibonacci Series

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The Fibonacci Series of the first ${n}$ numbers is ?$0, 1, 1, 2, 3, 5, 8, 13, 21$
    \n", "signature": "(min_no=1):", "funcdef": "def"}, "mathgenerator.computer_science.modulo_division": {"fullname": "mathgenerator.computer_science.modulo_division", "modulename": "mathgenerator.computer_science", "qualname": "modulo_division", "kind": "function", "doc": "

    Modulo Division

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $43$ % $33 = $$10$
    \n", "signature": "(max_res=99, max_modulo=99):", "funcdef": "def"}, "mathgenerator.computer_science.nth_fibonacci_number": {"fullname": "mathgenerator.computer_science.nth_fibonacci_number", "modulename": "mathgenerator.computer_science", "qualname": "nth_fibonacci_number", "kind": "function", "doc": "

    nth Fibonacci number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the 85th Fibonacci number?$259695496911123328$
    \n", "signature": "(max_n=100):", "funcdef": "def"}, "mathgenerator.computer_science.nth_tribonacci_number": {"fullname": "mathgenerator.computer_science.nth_tribonacci_number", "modulename": "mathgenerator.computer_science", "qualname": "nth_tribonacci_number", "kind": "function", "doc": "

    nth Tribonacci number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the 14th Tribonacci number?$504$
    \n", "signature": "(min_length=1, max_length=80):", "funcdef": "def"}, "mathgenerator.computer_science.tribonacci_series": {"fullname": "mathgenerator.computer_science.tribonacci_series", "modulename": "mathgenerator.computer_science", "qualname": "tribonacci_series", "kind": "function", "doc": "

    Fibonacci Series

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The Tribonacci Series of the first $8$ numbers is ?$0, 0, 1, 1, 2, 4, 7, 13$
    \n", "signature": "(min_length=1, max_length=80):", "funcdef": "def"}, "mathgenerator.geometry": {"fullname": "mathgenerator.geometry", "modulename": "mathgenerator.geometry", "kind": "module", "doc": "

    \n"}, "mathgenerator.geometry.angle_btw_vectors": {"fullname": "mathgenerator.geometry.angle_btw_vectors", "modulename": "mathgenerator.geometry", "qualname": "angle_btw_vectors", "kind": "function", "doc": "

    Angle between 2 vectors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    angle between the vectors $[363.84, 195.54, 997.08, 39.26, 60.14, 722.7, 888.57, 713.15, 436.22, 712.23, 349.23, 595.91, 191.8, 824.58, 861.56, 122.73, 815.14, 700.68, 506.5]$ and $[760.85, 934.67, 513.37, 796.93, 809.97, 423.54, 162.69, 758.96, 133.42, 478.14, 771.84, 824.88, 483.07, 134.41, 954.41, 893.42, 191.01, 453.97, 648.59]$ is:$0.81$ radians
    \n", "signature": "(max_elt_amt=20):", "funcdef": "def"}, "mathgenerator.geometry.angle_regular_polygon": {"fullname": "mathgenerator.geometry.angle_regular_polygon", "modulename": "mathgenerator.geometry", "qualname": "angle_regular_polygon", "kind": "function", "doc": "

    Angle of a Regular Polygon

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the angle of a regular polygon with $8$ sides$135.0$
    \n", "signature": "(min_val=3, max_val=20):", "funcdef": "def"}, "mathgenerator.geometry.arc_length": {"fullname": "mathgenerator.geometry.arc_length", "modulename": "mathgenerator.geometry", "qualname": "arc_length", "kind": "function", "doc": "

    Arc length of Angle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given radius, $44$ and angle, $184$. Find the arc length of the angle.Arc length of the angle $= 141.30186$
    \n", "signature": "(max_radius=49, max_angle=359):", "funcdef": "def"}, "mathgenerator.geometry.area_of_circle": {"fullname": "mathgenerator.geometry.area_of_circle", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle", "kind": "function", "doc": "

    Area of Circle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of circle with radius $29=$$2642.08$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.geometry.area_of_circle_given_center_and_point": {"fullname": "mathgenerator.geometry.area_of_circle_given_center_and_point", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle_given_center_and_point", "kind": "function", "doc": "

    Area of Circle given center and a point on circle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of circle with center $(7,-6)$ and passing through $(1.0, -6.0)$ is$113.1$
    \n", "signature": "(max_coordinate=10, max_radius=10):", "funcdef": "def"}, "mathgenerator.geometry.area_of_trapezoid": {"fullname": "mathgenerator.geometry.area_of_trapezoid", "modulename": "mathgenerator.geometry", "qualname": "area_of_trapezoid", "kind": "function", "doc": "

    Area of Trapezoid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of trapezoid with height $12$ and base lengths: $3, 7, = $$60$
    \n", "signature": "(max_len=20):", "funcdef": "def"}, "mathgenerator.geometry.area_of_triangle": {"fullname": "mathgenerator.geometry.area_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "area_of_triangle", "kind": "function", "doc": "

    Area of Triangle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of triangle with side lengths: $8, 1, 8 = $$3.99$
    \n", "signature": "(max_a=20, max_b=20):", "funcdef": "def"}, "mathgenerator.geometry.basic_trigonometry": {"fullname": "mathgenerator.geometry.basic_trigonometry", "modulename": "mathgenerator.geometry", "qualname": "basic_trigonometry", "kind": "function", "doc": "

    Trigonometric Values

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\sin(30) = $$\\frac{1}{2}$
    \n", "signature": "(angles=[0, 30, 45, 60, 90], functions=['sin', 'cos', 'tan']):", "funcdef": "def"}, "mathgenerator.geometry.circumference": {"fullname": "mathgenerator.geometry.circumference", "modulename": "mathgenerator.geometry", "qualname": "circumference", "kind": "function", "doc": "

    Circumference of Circle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Circumference of circle with radius $56 = $$351.86$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.geometry.complementary_and_supplementary_angle": {"fullname": "mathgenerator.geometry.complementary_and_supplementary_angle", "modulename": "mathgenerator.geometry", "qualname": "complementary_and_supplementary_angle", "kind": "function", "doc": "

    Complementary and Supplementary Angle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The complementary angle of $15 =$$75$
    \n", "signature": "(max_supp=180, max_comp=90):", "funcdef": "def"}, "mathgenerator.geometry.curved_surface_area_cylinder": {"fullname": "mathgenerator.geometry.curved_surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "curved_surface_area_cylinder", "kind": "function", "doc": "

    Curved surface area of a cylinder

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the curved surface area of a cylinder of radius, $44$ and height, $92$?$25434.33$
    \n", "signature": "(max_radius=49, max_height=99):", "funcdef": "def"}, "mathgenerator.geometry.degree_to_rad": {"fullname": "mathgenerator.geometry.degree_to_rad", "modulename": "mathgenerator.geometry", "qualname": "degree_to_rad", "kind": "function", "doc": "

    Degrees to Radians

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Angle $113$ degrees in radians is:$1.97$
    \n", "signature": "(max_deg=360):", "funcdef": "def"}, "mathgenerator.geometry.equation_of_line_from_two_points": {"fullname": "mathgenerator.geometry.equation_of_line_from_two_points", "modulename": "mathgenerator.geometry", "qualname": "equation_of_line_from_two_points", "kind": "function", "doc": "

    Equation of line from two points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the equation of the line between points $(13,9)$ and $(6,-19)$ in slope-intercept form?$y = 4x -43$
    \n", "signature": "(max_coordinate=20, min_coordinate=-20):", "funcdef": "def"}, "mathgenerator.geometry.fourth_angle_of_quadrilateral": {"fullname": "mathgenerator.geometry.fourth_angle_of_quadrilateral", "modulename": "mathgenerator.geometry", "qualname": "fourth_angle_of_quadrilateral", "kind": "function", "doc": "

    Fourth Angle of Quadrilateral

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Fourth angle of quadrilateral with angles $162 , 43, 78 =$$77$
    \n", "signature": "(max_angle=180):", "funcdef": "def"}, "mathgenerator.geometry.perimeter_of_polygons": {"fullname": "mathgenerator.geometry.perimeter_of_polygons", "modulename": "mathgenerator.geometry", "qualname": "perimeter_of_polygons", "kind": "function", "doc": "

    Perimeter of Polygons

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The perimeter of a $4$ sided polygon with lengths of $30, 105, 78, 106$cm is:$319$
    \n", "signature": "(max_sides=12, max_length=120):", "funcdef": "def"}, "mathgenerator.geometry.pythagorean_theorem": {"fullname": "mathgenerator.geometry.pythagorean_theorem", "modulename": "mathgenerator.geometry", "qualname": "pythagorean_theorem", "kind": "function", "doc": "

    Pythagorean Theorem

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the hypotenuse of a right triangle given the other two sides have lengths $9$ and $10$?$13.45$
    \n", "signature": "(max_length=20):", "funcdef": "def"}, "mathgenerator.geometry.radian_to_deg": {"fullname": "mathgenerator.geometry.radian_to_deg", "modulename": "mathgenerator.geometry", "qualname": "radian_to_deg", "kind": "function", "doc": "

    Radians to Degrees

    \n", "signature": "(max_rad=6.28):", "funcdef": "def"}, "mathgenerator.geometry.sector_area": {"fullname": "mathgenerator.geometry.sector_area", "modulename": "mathgenerator.geometry", "qualname": "sector_area", "kind": "function", "doc": "

    Area of a Sector

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the area of a sector with radius $42$ and angle $83$ degrees?$1277.69$
    \n", "signature": "(max_radius=49, max_angle=359):", "funcdef": "def"}, "mathgenerator.geometry.sum_of_polygon_angles": {"fullname": "mathgenerator.geometry.sum_of_polygon_angles", "modulename": "mathgenerator.geometry", "qualname": "sum_of_polygon_angles", "kind": "function", "doc": "

    Sum of Angles of Polygon

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the sum of interior angles of a polygon with $8$ sides?$1080$
    \n", "signature": "(max_sides=12):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cone": {"fullname": "mathgenerator.geometry.surface_area_cone", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cone", "kind": "function", "doc": "

    Surface area of a cone

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cone with height $= 26m$ and radius $= 6m$ is$616 m^2$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cube": {"fullname": "mathgenerator.geometry.surface_area_cube", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cube", "kind": "function", "doc": "

    Surface area of a cube

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cube with side $= 6m$ is$216 m^2$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cuboid": {"fullname": "mathgenerator.geometry.surface_area_cuboid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cuboid", "kind": "function", "doc": "

    Surface area of a cuboid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cuboid with sides of lengths: $11m, 20m, 8m$ is$936 m^2$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cylinder": {"fullname": "mathgenerator.geometry.surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cylinder", "kind": "function", "doc": "

    Surface area of a cylinder

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cylinder with height $= 26m$ and radius $= 15m$ is$3864 m^2$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_pyramid": {"fullname": "mathgenerator.geometry.surface_area_pyramid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_pyramid", "kind": "function", "doc": "

    Surface area of a pyramid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of pyramid with base length $= 30m$, base width $= 40m$, and height $= 25m$ is$2400 m^2$
    \n", "signature": "(unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_sphere": {"fullname": "mathgenerator.geometry.surface_area_sphere", "modulename": "mathgenerator.geometry", "qualname": "surface_area_sphere", "kind": "function", "doc": "

    Surface area of a sphere

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of a sphere with radius $= 8m$ is$804.25 m^2$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.third_angle_of_triangle": {"fullname": "mathgenerator.geometry.third_angle_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "third_angle_of_triangle", "kind": "function", "doc": "

    Third Angle of Triangle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Third angle of triangle with angles $10$ and $22 =$$148$
    \n", "signature": "(max_angle=89):", "funcdef": "def"}, "mathgenerator.geometry.valid_triangle": {"fullname": "mathgenerator.geometry.valid_triangle", "modulename": "mathgenerator.geometry", "qualname": "valid_triangle", "kind": "function", "doc": "

    Valid Triangle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Does triangel with sides $10, 31$ and $14$ exist?No
    \n", "signature": "(max_side_length=50):", "funcdef": "def"}, "mathgenerator.geometry.volume_cone": {"fullname": "mathgenerator.geometry.volume_cone", "modulename": "mathgenerator.geometry", "qualname": "volume_cone", "kind": "function", "doc": "

    Volume of a cone

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of cone with height $= 44m$ and radius $= 11m$ is$5575 m^3$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cube": {"fullname": "mathgenerator.geometry.volume_cube", "modulename": "mathgenerator.geometry", "qualname": "volume_cube", "kind": "function", "doc": "

    Volume of a cube

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of a cube with a side length of $19m$ is$6859 m^3$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cuboid": {"fullname": "mathgenerator.geometry.volume_cuboid", "modulename": "mathgenerator.geometry", "qualname": "volume_cuboid", "kind": "function", "doc": "

    Volume of a cuboid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of cuboid with sides = $17m, 11m, 13m$ is$2431 m^3$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cylinder": {"fullname": "mathgenerator.geometry.volume_cylinder", "modulename": "mathgenerator.geometry", "qualname": "volume_cylinder", "kind": "function", "doc": "

    Volume of a cylinder

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of cylinder with height $= 3m$ and radius $= 10m$ is$942 m^3$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cone_frustum": {"fullname": "mathgenerator.geometry.volume_cone_frustum", "modulename": "mathgenerator.geometry", "qualname": "volume_cone_frustum", "kind": "function", "doc": "

    Volume of the frustum of a cone

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is$19603.54 m^3$
    \n", "signature": "(max_r1=20, max_r2=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_hemisphere": {"fullname": "mathgenerator.geometry.volume_hemisphere", "modulename": "mathgenerator.geometry", "qualname": "volume_hemisphere", "kind": "function", "doc": "

    Volume of a hemisphere

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of hemisphere with radius $32m =$$68629.14 m^3$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.geometry.volume_pyramid": {"fullname": "mathgenerator.geometry.volume_pyramid", "modulename": "mathgenerator.geometry", "qualname": "volume_pyramid", "kind": "function", "doc": "

    Volume of a pyramid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is$1764.0 m^3$
    \n", "signature": "(max_length=20, max_width=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_sphere": {"fullname": "mathgenerator.geometry.volume_sphere", "modulename": "mathgenerator.geometry", "qualname": "volume_sphere", "kind": "function", "doc": "

    Volume of a sphere

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of sphere with radius $30 m = $$113097.36 m^3$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.misc": {"fullname": "mathgenerator.misc", "modulename": "mathgenerator.misc", "kind": "module", "doc": "

    \n"}, "mathgenerator.misc.arithmetic_progression_sum": {"fullname": "mathgenerator.misc.arithmetic_progression_sum", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_sum", "kind": "function", "doc": "

    Arithmetic Progression Sum

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the sum of first $44$ terms of the AP series: $49, 145, 241 ... $$92972.0$
    \n", "signature": "(max_d=100, max_a=100, max_n=100):", "funcdef": "def"}, "mathgenerator.misc.arithmetic_progression_term": {"fullname": "mathgenerator.misc.arithmetic_progression_term", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_term", "kind": "function", "doc": "

    Arithmetic Progression Term

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find term number $12$ of the AP series: $-54, 24, 102 ... $$804$
    \n", "signature": "(max_d=100, max_a=100, max_n=100):", "funcdef": "def"}, "mathgenerator.misc.base_conversion": {"fullname": "mathgenerator.misc.base_conversion", "modulename": "mathgenerator.misc", "qualname": "base_conversion", "kind": "function", "doc": "

    Base Conversion

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Convert $45204$ from base $10$ to base $4$$23002110$
    \n", "signature": "(max_num=60000, max_base=16):", "funcdef": "def"}, "mathgenerator.misc.binomial_distribution": {"fullname": "mathgenerator.misc.binomial_distribution", "modulename": "mathgenerator.misc", "qualname": "binomial_distribution", "kind": "function", "doc": "

    Binomial distribution

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    A manufacturer of metal pistons finds that, on average, $30.56$% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of $20$ pistons will contain no more than $2$ rejected pistons?$3.17$
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.misc.celsius_to_fahrenheit": {"fullname": "mathgenerator.misc.celsius_to_fahrenheit", "modulename": "mathgenerator.misc", "qualname": "celsius_to_fahrenheit", "kind": "function", "doc": "

    Celsius to Fahrenheit

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Convert $-46$ degrees Celsius to degrees Fahrenheit$-50.8$
    \n", "signature": "(max_temp=100):", "funcdef": "def"}, "mathgenerator.misc.common_factors": {"fullname": "mathgenerator.misc.common_factors", "modulename": "mathgenerator.misc", "qualname": "common_factors", "kind": "function", "doc": "

    Common Factors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Common Factors of $100$ and $44 = $$[1, 2, 4]$
    \n", "signature": "(max_val=100):", "funcdef": "def"}, "mathgenerator.misc.complex_to_polar": {"fullname": "mathgenerator.misc.complex_to_polar", "modulename": "mathgenerator.misc", "qualname": "complex_to_polar", "kind": "function", "doc": "

    Complex to polar form

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $19.42(-19.0\\theta + i-4.0\\theta)$$-2.93$
    \n", "signature": "(min_real_imaginary_num=-20, max_real_imaginary_num=20):", "funcdef": "def"}, "mathgenerator.misc.decimal_to_roman_numerals": {"fullname": "mathgenerator.misc.decimal_to_roman_numerals", "modulename": "mathgenerator.misc", "qualname": "decimal_to_roman_numerals", "kind": "function", "doc": "

    Decimal to Roman Numerals

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The number $92$ in roman numerals is:$XCII$
    \n", "signature": "(max_decimal=3999):", "funcdef": "def"}, "mathgenerator.misc.euclidian_norm": {"fullname": "mathgenerator.misc.euclidian_norm", "modulename": "mathgenerator.misc", "qualname": "euclidian_norm", "kind": "function", "doc": "

    Euclidian norm or L2 norm of a vector

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Euclidian norm or L2 norm of the vector $[659.9225071540442, 243.40887829281564, 128.79950053874424, 263.19226900031344]$ is:$761.97$
    \n", "signature": "(maxEltAmt=20):", "funcdef": "def"}, "mathgenerator.misc.factors": {"fullname": "mathgenerator.misc.factors", "modulename": "mathgenerator.misc", "qualname": "factors", "kind": "function", "doc": "

    Factors of a number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Factors of $176 = $$[1, 2, 4, 8, 11, 16, 22, 44, 88, 176]$
    \n", "signature": "(max_val=1000):", "funcdef": "def"}, "mathgenerator.misc.geometric_mean": {"fullname": "mathgenerator.misc.geometric_mean", "modulename": "mathgenerator.misc", "qualname": "geometric_mean", "kind": "function", "doc": "

    Geometric Mean of N Numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Geometric mean of $3$ numbers $[72, 21, 87] = $$50.86$
    \n", "signature": "(max_value=100, max_count=4):", "funcdef": "def"}, "mathgenerator.misc.geometric_progression": {"fullname": "mathgenerator.misc.geometric_progression", "modulename": "mathgenerator.misc", "qualname": "geometric_progression", "kind": "function", "doc": "

    Geometric Progression

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    For the given GP $[11, 44, 176, 704, 2816, 11264]$. Find the value of a common ratio, 7th term value, sum upto 10th termThe value of a is $11$, common ratio is $4$ , 7th term is $45056$, sum upto 10th term is $3844775.0$
    \n", "signature": "(number_values=6, min_value=2, max_value=12, n_term=7, sum_term=5):", "funcdef": "def"}, "mathgenerator.misc.harmonic_mean": {"fullname": "mathgenerator.misc.harmonic_mean", "modulename": "mathgenerator.misc", "qualname": "harmonic_mean", "kind": "function", "doc": "

    Harmonic Mean of N Numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Harmonic mean of $4$ numbers $52, 56, 25, 57 = $$602.33$
    \n", "signature": "(max_value=100, max_count=4):", "funcdef": "def"}, "mathgenerator.misc.is_leap_year": {"fullname": "mathgenerator.misc.is_leap_year", "modulename": "mathgenerator.misc", "qualname": "is_leap_year", "kind": "function", "doc": "

    Is Leap Year or Not

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Is $2000$ a leap year?$2000$ is a leap year
    \n", "signature": "(minNumber=1900, max_number=2099):", "funcdef": "def"}, "mathgenerator.misc.lcm": {"fullname": "mathgenerator.misc.lcm", "modulename": "mathgenerator.misc", "qualname": "lcm", "kind": "function", "doc": "

    LCM (Least Common Multiple)

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    LCM of $3$ and $18 = $$18$
    \n", "signature": "(max_val=20):", "funcdef": "def"}, "mathgenerator.misc.minutes_to_hours": {"fullname": "mathgenerator.misc.minutes_to_hours", "modulename": "mathgenerator.misc", "qualname": "minutes_to_hours", "kind": "function", "doc": "

    Convert minutes to hours and minutes

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Convert $836$ minutes to hours & minutes$13$ hours and $56$ minutes
    \n", "signature": "(max_minutes=999):", "funcdef": "def"}, "mathgenerator.misc.prime_factors": {"fullname": "mathgenerator.misc.prime_factors", "modulename": "mathgenerator.misc", "qualname": "prime_factors", "kind": "function", "doc": "

    Prime Factors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find prime factors of $30$$2, 3, 5$
    \n", "signature": "(min_val=1, max_val=200):", "funcdef": "def"}, "mathgenerator.misc.product_of_scientific_notations": {"fullname": "mathgenerator.misc.product_of_scientific_notations", "modulename": "mathgenerator.misc", "qualname": "product_of_scientific_notations", "kind": "function", "doc": "

    Product of scientific notations

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Product of scientific notations $5.11 \\times 10^{67}$ and $3.64 \\times 10^{-59} = $$1.86 \\times 10^{9}$
    \n", "signature": "(min_exp_val=-100, max_exp_val=100):", "funcdef": "def"}, "mathgenerator.misc.profit_loss_percent": {"fullname": "mathgenerator.misc.profit_loss_percent", "modulename": "mathgenerator.misc", "qualname": "profit_loss_percent", "kind": "function", "doc": "

    Profit or Loss Percent

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Loss percent when $CP = 751$ and $SP = 290$ is:$61.38$
    \n", "signature": "(max_cp=1000, max_sp=1000):", "funcdef": "def"}, "mathgenerator.misc.quotient_of_power_same_base": {"fullname": "mathgenerator.misc.quotient_of_power_same_base", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_base", "kind": "function", "doc": "

    Quotient of Powers with Same Base

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The Quotient of $5^{6}$ and $5^{8} = 5^{6-8} = 5^{-2}$$0.04$
    \n", "signature": "(max_base=50, max_power=10):", "funcdef": "def"}, "mathgenerator.misc.quotient_of_power_same_power": {"fullname": "mathgenerator.misc.quotient_of_power_same_power", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_power", "kind": "function", "doc": "

    Quotient of Powers with Same Power

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The quotient of $19^{8}$ and $10^{8} = (19/10)^8 = 1.9^{8}$$169.84$
    \n", "signature": "(max_base=50, max_power=10):", "funcdef": "def"}, "mathgenerator.misc.set_operation": {"fullname": "mathgenerator.misc.set_operation", "modulename": "mathgenerator.misc", "qualname": "set_operation", "kind": "function", "doc": "

    Union, Intersection, Difference of Two Sets

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}$. Find the Union, intersection, $a-b$, $b-a$, and symmetric differenceUnion is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, $a-b$ is ${4, 5}$, $b-a$ is ${8}$. Symmetric difference is ${4, 5, 8}$.
    \n", "signature": "(min_size=3, max_size=7):", "funcdef": "def"}, "mathgenerator.misc.signum_function": {"fullname": "mathgenerator.misc.signum_function", "modulename": "mathgenerator.misc", "qualname": "signum_function", "kind": "function", "doc": "

    Signum Function

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Signum of $-229$ is =$-1$
    \n", "signature": "(min=-999, max=999):", "funcdef": "def"}, "mathgenerator.misc.surds_comparison": {"fullname": "mathgenerator.misc.surds_comparison", "modulename": "mathgenerator.misc", "qualname": "surds_comparison", "kind": "function", "doc": "

    Comparing Surds

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Fill in the blanks $42^{\\frac{1}{2}}$ _ $45^{\\frac{1}{5}}$$>$
    \n", "signature": "(max_value=100, max_root=10):", "funcdef": "def"}, "mathgenerator.misc.velocity_of_object": {"fullname": "mathgenerator.misc.velocity_of_object", "modulename": "mathgenerator.misc", "qualname": "velocity_of_object", "kind": "function", "doc": "

    Velocity of object

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    An object travels at uniform velocity a distance of $100 m$ in $4$ seconds. What is the velocity of the car?$25 m/s$
    \n", "signature": "(max_displacement=1000, max_time=100):", "funcdef": "def"}, "mathgenerator.physics": {"fullname": "mathgenerator.physics", "modulename": "mathgenerator.physics", "kind": "module", "doc": "

    \n"}, "mathgenerator.physics.kinetic_energy": {"fullname": "mathgenerator.physics.kinetic_energy", "modulename": "mathgenerator.physics", "qualname": "kinetic_energy", "kind": "function", "doc": "

    Kinetic Energy calculation using Ek = 0.5 * m * v^2

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$$250 J$
    \n", "signature": "(max_mass=1000, max_vel=100):", "funcdef": "def"}, "mathgenerator.physics.potential_dividers": {"fullname": "mathgenerator.physics.potential_dividers", "modulename": "mathgenerator.physics", "qualname": "potential_dividers", "kind": "function", "doc": "

    Potential Divider question using Vout = (Vin * R2) / (R2 + R1)

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    In a Potential Divider, if resistors R1 and R2 have resistances of $100 \u2126$ and $50 \u2126$ respectively, and the cell has $12 V$ What is the output potential difference across R2?$4 V$
    \n", "signature": "(max_vin=50, max_resistance=500):", "funcdef": "def"}, "mathgenerator.physics.resistivity": {"fullname": "mathgenerator.physics.resistivity", "modulename": "mathgenerator.physics", "qualname": "resistivity", "kind": "function", "doc": "

    Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    A wire has resistance $30 m\u2126$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire$6.14e-07 \u2126m$
    \n", "signature": "(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):", "funcdef": "def"}, "mathgenerator.statistics": {"fullname": "mathgenerator.statistics", "modulename": "mathgenerator.statistics", "kind": "module", "doc": "

    \n"}, "mathgenerator.statistics.combinations": {"fullname": "mathgenerator.statistics.combinations", "modulename": "mathgenerator.statistics", "qualname": "combinations", "kind": "function", "doc": "

    Combinations of Objects

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the number of combinations from $19$ objects picked $6$ at a time.$27132$
    \n", "signature": "(max_lengthgth=20):", "funcdef": "def"}, "mathgenerator.statistics.conditional_probability": {"fullname": "mathgenerator.statistics.conditional_probability", "modulename": "mathgenerator.statistics", "qualname": "conditional_probability", "kind": "function", "doc": "

    Conditional Probability

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Someone tested positive for a nasty disease which only $1.18$% of the population have. Test sensitivity (true positive) is equal to $SN=98.73$% whereas test specificity (true negative) $SP=99.99$%. What is the probability that this guy really has that disease?$99.16$%
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.statistics.confidence_interval": {"fullname": "mathgenerator.statistics.confidence_interval", "modulename": "mathgenerator.statistics", "qualname": "confidence_interval", "kind": "function", "doc": "

    Confidence interval For sample S

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The confidence interval for sample $[234, 223, 210, 203, 258, 299, 281, 208, 278, 252, 295, 245, 280, 235, 219, 297, 214, 267, 212, 256, 232, 221]$ with $99$% confidence is$(263.31, 229.33)$
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.statistics.data_summary": {"fullname": "mathgenerator.statistics.data_summary", "modulename": "mathgenerator.statistics", "qualname": "data_summary", "kind": "function", "doc": "

    Mean, Standard Deviation and Variance

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the mean,standard deviation and variance for the data $9, 29, 46, 27, 46, 15, 10, 44, 19, 33, 38, 7, 34, 28, 8$The Mean is $26.2$, Standard Deviation is $186.29$, Variance is $13.65$
    \n", "signature": "(number_values=15, min_val=5, max_val=50):", "funcdef": "def"}, "mathgenerator.statistics.dice_sum_probability": {"fullname": "mathgenerator.statistics.dice_sum_probability", "modulename": "mathgenerator.statistics", "qualname": "dice_sum_probability", "kind": "function", "doc": "

    Probability of a certain sum appearing on faces of dice

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    If $2$ dice are rolled at the same time, the probability of getting a sum of $5 =$$\\frac{4}{36}$
    \n", "signature": "(max_dice=3):", "funcdef": "def"}, "mathgenerator.statistics.mean_median": {"fullname": "mathgenerator.statistics.mean_median", "modulename": "mathgenerator.statistics", "qualname": "mean_median", "kind": "function", "doc": "

    Mean and Median

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given the series of numbers $[4, 19, 21, 22, 43, 44, 60, 81, 87, 92]$. Find the arithmatic mean and median of the seriesArithmetic mean of the series is $47.3$ and arithmetic median of this series is $43.5$
    \n", "signature": "(max_length=10):", "funcdef": "def"}, "mathgenerator.statistics.permutation": {"fullname": "mathgenerator.statistics.permutation", "modulename": "mathgenerator.statistics", "qualname": "permutation", "kind": "function", "doc": "

    Permutations

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Number of Permutations from $18$ objects picked $5$ at a time is:$1028160$
    \n", "signature": "(max_lengthgth=20):", "funcdef": "def"}}, "docInfo": {"mathgenerator": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 586}, "mathgenerator.get_gen_list": {"qualname": 3, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 7, "bases": 0, "doc": 3}, "mathgenerator.gen_by_id": {"qualname": 3, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 25, "bases": 0, "doc": 3}, "mathgenerator.getGenList": {"qualname": 1, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 7, "bases": 0, "doc": 3}, "mathgenerator.genById": {"qualname": 1, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 25, "bases": 0, "doc": 3}, "mathgenerator.algebra": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "mathgenerator.algebra.basic_algebra": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 17, 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"fullname": 6, "annotation": 0, "default_value": 0, "signature": 18, "bases": 0, "doc": 50}, "mathgenerator.algebra.intersection_of_two_lines": {"qualname": 4, "fullname": 6, "annotation": 0, "default_value": 0, "signature": 78, "bases": 0, "doc": 61}, "mathgenerator.algebra.invert_matrix": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 48, "bases": 0, "doc": 78}, "mathgenerator.algebra.linear_equations": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 38, "bases": 0, "doc": 58}, "mathgenerator.algebra.line_equation_from_2_points": {"qualname": 5, "fullname": 7, "annotation": 0, "default_value": 0, "signature": 17, "bases": 0, "doc": 62}, "mathgenerator.algebra.log": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 28, "bases": 0, "doc": 40}, "mathgenerator.algebra.matrix_multiplication": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 28, "bases": 0, 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"mathgenerator.basic_math.cube_root": {"qualname": 2, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 28, "bases": 0, "doc": 49}, "mathgenerator.basic_math.divide_fractions": {"qualname": 2, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 17, "bases": 0, "doc": 39}, "mathgenerator.basic_math.division": {"qualname": 1, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 28, "bases": 0, "doc": 38}, "mathgenerator.basic_math.exponentiation": {"qualname": 1, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 28, "bases": 0, "doc": 38}, "mathgenerator.basic_math.factorial": {"qualname": 1, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 17, "bases": 0, "doc": 38}, "mathgenerator.basic_math.fraction_multiplication": {"qualname": 2, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 17, "bases": 0, "doc": 39}, "mathgenerator.basic_math.fraction_to_decimal": {"qualname": 3, "fullname": 6, "annotation": 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    mathgenerator

    \n\n

    Fork of https://github.com/lukew3/mathgenerator
    \nAdding more Physics and Computer Science questions

    \n\n

    A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.

    \n\n

    To try out generators, go to https://mathgenerator-demo.netlify.app

    \n\n

    See CONTRIBUTING.md for information about how to contribute.

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    Table of Contents

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    Installation

    \n\n

    The project can be install via pip

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    \n
    pip install mathgenerator\n
    \n
    \n\n

    Usage

    \n\n

    Here is an example of how you would generate an addition problem:

    \n\n
    \n
    import mathgenerator\n\n#generate an addition problem\nproblem, solution = mathgenerator.addition()\n\n#another way to generate an addition problem using genById()\nproblem, solution = mathgenerator.genById(0)\n
    \n
    \n\n

    You may prefer to use import mathgenerator as mg and run functions like mg.addition() so that you don't have to type as much.\n\nProblem/solution pairs are generated with either:

    \n\n
      \n
    • mathgenerator.<generator_name>() - generates a problem, solution set from the given generator name.
      • \n
    • mathgenerator.genById(id) - generates a problem, solution set with generator id provided by the id parameter
      • \n
    \n\n

    \nYou can also use getGenList() to return a list of all generators included in the library in the format:\n\n\n

    [funcname, subjectname]\n
    \n\n

    Documentation

    \n\n

    Documentation can be found at https://lukew3.github.io/mathgenerator

    \n"}, "mathgenerator.get_gen_list": {"fullname": "mathgenerator.get_gen_list", "modulename": "mathgenerator", "qualname": "get_gen_list", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.gen_by_id": {"fullname": "mathgenerator.gen_by_id", "modulename": "mathgenerator", "qualname": "gen_by_id", "kind": "function", "doc": "

    \n", "signature": "(id, *args, **kwargs):", "funcdef": "def"}, "mathgenerator.getGenList": {"fullname": "mathgenerator.getGenList", "modulename": "mathgenerator", "qualname": "getGenList", "kind": "function", "doc": "

    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.genById": {"fullname": "mathgenerator.genById", "modulename": "mathgenerator", "qualname": "genById", "kind": "function", "doc": "

    \n", "signature": "(id, *args, **kwargs):", "funcdef": "def"}, "mathgenerator.algebra": {"fullname": "mathgenerator.algebra", "modulename": "mathgenerator.algebra", "kind": "module", "doc": "

    \n"}, "mathgenerator.algebra.basic_algebra": {"fullname": "mathgenerator.algebra.basic_algebra", "modulename": "mathgenerator.algebra", "qualname": "basic_algebra", "kind": "function", "doc": "

    Basic Algebra

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $1x + 5 = 5$$0$
    \n", "signature": "(max_variable=10):", "funcdef": "def"}, "mathgenerator.algebra.combine_like_terms": {"fullname": "mathgenerator.algebra.combine_like_terms", "modulename": "mathgenerator.algebra", "qualname": "combine_like_terms", "kind": "function", "doc": "

    Combine Like Terms

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $6x^{9} + 3x^{2} + 5x^{19} + 3x^{17}$$3x^{2} + 6x^{9} + 3x^{17} + 5x^{19}$
    \n", "signature": "(max_coef=10, max_exp=20, max_terms=10):", "funcdef": "def"}, "mathgenerator.algebra.complex_quadratic": {"fullname": "mathgenerator.algebra.complex_quadratic", "modulename": "mathgenerator.algebra", "qualname": "complex_quadratic", "kind": "function", "doc": "

    Complex Quadratic Equation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the roots of given Quadratic Equation $x^2 + 8x + 8 = 0$$((-1.172, -6.828)) = (\\frac{-8 + \\sqrt{32}}{2}, (\\frac{-8 - \\sqrt{32}}{2})$
    \n", "signature": "(prob_type=0, max_range=10):", "funcdef": "def"}, "mathgenerator.algebra.compound_interest": {"fullname": "mathgenerator.algebra.compound_interest", "modulename": "mathgenerator.algebra", "qualname": "compound_interest", "kind": "function", "doc": "

    Compound Interest

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Compound interest for a principle amount of $2679$ dollars, $9$% rate of interest and for a time period of $3$ years is $=$$3469.38$
    \n", "signature": "(max_principle=10000, max_rate=10, max_time=10):", "funcdef": "def"}, "mathgenerator.algebra.distance_two_points": {"fullname": "mathgenerator.algebra.distance_two_points", "modulename": "mathgenerator.algebra", "qualname": "distance_two_points", "kind": "function", "doc": "

    Distance between 2 points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the distance between $(-19, -6)$ and $(15, -16)$$\\sqrt{1256}$
    \n", "signature": "(max_val_xy=20, min_val_xy=-20):", "funcdef": "def"}, "mathgenerator.algebra.expanding": {"fullname": "mathgenerator.algebra.expanding", "modulename": "mathgenerator.algebra", "qualname": "expanding", "kind": "function", "doc": "

    Expanding Factored Binomial

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $(x-6)(-3x-3)$$x^2+18x+18$
    \n", "signature": "(range_x1=10, range_x2=10, range_a=10, range_b=10):", "funcdef": "def"}, "mathgenerator.algebra.factoring": {"fullname": "mathgenerator.algebra.factoring", "modulename": "mathgenerator.algebra", "qualname": "factoring", "kind": "function", "doc": "

    Factoring Quadratic\nGiven a quadratic equation in the form x^2 + bx + c, factor it into it's roots (x - x1)(x -x2)

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $x^2+2x-24$$(x-4)(x+6)$
    \n", "signature": "(range_x1=10, range_x2=10):", "funcdef": "def"}, "mathgenerator.algebra.int_matrix_22_determinant": {"fullname": "mathgenerator.algebra.int_matrix_22_determinant", "modulename": "mathgenerator.algebra", "qualname": "int_matrix_22_determinant", "kind": "function", "doc": "

    Determinant to 2x2 Matrix

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\det \\begin{bmatrix} 88 & 40 \\\\ 9 & 91 \\end{bmatrix}= $$7648$
    \n", "signature": "(max_matrix_val=100):", "funcdef": "def"}, "mathgenerator.algebra.intersection_of_two_lines": {"fullname": "mathgenerator.algebra.intersection_of_two_lines", "modulename": "mathgenerator.algebra", "qualname": "intersection_of_two_lines", "kind": "function", "doc": "

    Intersection of two lines

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the point of intersection of the two lines: $y = \\frac{-2}{6}x + 3$ and $y = \\frac{3}{6}x - 8$$(\\frac{66}{5}, \\frac{-7}{5})$
    \n", "signature": "(\tmin_m=-10,\tmax_m=10,\tmin_b=-10,\tmax_b=10,\tmin_denominator=1,\tmax_denominator=6):", "funcdef": "def"}, "mathgenerator.algebra.invert_matrix": {"fullname": "mathgenerator.algebra.invert_matrix", "modulename": "mathgenerator.algebra", "qualname": "invert_matrix", "kind": "function", "doc": "

    Invert Matrix

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Inverse of Matrix $\\begin{bmatrix} 4 & 1 & 4 \\\\ 5 & 1 & 5 \\\\ 12 & 3 & 13 \\end{bmatrix}$ is:$\\begin{bmatrix} 2 & 1 & -1 \\\\ 5 & -4 & 0 \\\\ -3 & 0 & 1 \\end{bmatrix}$
    \n", "signature": "(\tsquare_matrix_dimension=3,\tmax_matrix_element=99,\tonly_integer_elements_in_inverted_matrixe=True):", "funcdef": "def"}, "mathgenerator.algebra.linear_equations": {"fullname": "mathgenerator.algebra.linear_equations", "modulename": "mathgenerator.algebra", "qualname": "linear_equations", "kind": "function", "doc": "

    Linear Equations

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given the equations $10x + -20y = 310$ and $-16x + -17y = 141$, solve for $x$ and $y$$x = 5$, $y = -13$
    \n", "signature": "(n=2, var_range=20, coeff_range=20):", "funcdef": "def"}, "mathgenerator.algebra.line_equation_from_2_points": {"fullname": "mathgenerator.algebra.line_equation_from_2_points", "modulename": "mathgenerator.algebra", "qualname": "line_equation_from_2_points", "kind": "function", "doc": "

    Equation of Line from Two Points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the equation of the line passing through the points $(-19,-8)$ and $(-2,0)$.$y=\\frac{8}{17}x+\\frac{16}{17}$
    \n", "signature": "(max_val=20):", "funcdef": "def"}, "mathgenerator.algebra.log": {"fullname": "mathgenerator.algebra.log", "modulename": "mathgenerator.algebra", "qualname": "log", "kind": "function", "doc": "

    Logarithm

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $log_{3}(243)=$$5$
    \n", "signature": "(max_base=3, max_val=8):", "funcdef": "def"}, "mathgenerator.algebra.matrix_multiplication": {"fullname": "mathgenerator.algebra.matrix_multiplication", "modulename": "mathgenerator.algebra", "qualname": "matrix_multiplication", "kind": "function", "doc": "

    Multiply Two Matrices

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Multiply $\\begin{bmatrix} 15 & 72 \\\\ 64 & -20 \\\\ 18 & 59 \\\\ -21 & -55 \\\\ 20 & -12 \\\\ -75 & -42 \\\\ 47 & 89 \\\\ -53 & 27 \\\\ -56 & 44 \\end{bmatrix}$ and $\\begin{bmatrix} 49 & -2 & 68 & -28 \\\\ 49 & 6 & 83 & 42 \\end{bmatrix}$$\\begin{bmatrix} 4263 & 402 & 6996 & 2604 \\\\ 2156 & -248 & 2692 & -2632 \\\\ 3773 & 318 & 6121 & 1974 \\\\ -3724 & -288 & -5993 & -1722 \\\\ 392 & -112 & 364 & -1064 \\\\ -5733 & -102 & -8586 & 336 \\\\ 6664 & 440 & 10583 & 2422 \\\\ -1274 & 268 & -1363 & 2618 \\\\ -588 & 376 & -156 & 3416 \\end{bmatrix}$
    \n", "signature": "(max_val=100, max_dim=10):", "funcdef": "def"}, "mathgenerator.algebra.midpoint_of_two_points": {"fullname": "mathgenerator.algebra.midpoint_of_two_points", "modulename": "mathgenerator.algebra", "qualname": "midpoint_of_two_points", "kind": "function", "doc": "

    Midpoint of two points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The midpoint of $(-8,10)$ and $(18,0) = $$(5.0,5.0)$
    \n", "signature": "(max_value=20):", "funcdef": "def"}, "mathgenerator.algebra.multiply_complex_numbers": {"fullname": "mathgenerator.algebra.multiply_complex_numbers", "modulename": "mathgenerator.algebra", "qualname": "multiply_complex_numbers", "kind": "function", "doc": "

    Multiplication of 2 complex numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $(14+18j) * (14+15j) = $$(-74+462j)$
    \n", "signature": "(min_real_imaginary_num=-20, max_real_imaginary_num=20):", "funcdef": "def"}, "mathgenerator.algebra.multiply_int_to_22_matrix": {"fullname": "mathgenerator.algebra.multiply_int_to_22_matrix", "modulename": "mathgenerator.algebra", "qualname": "multiply_int_to_22_matrix", "kind": "function", "doc": "

    Multiply Integer to 2x2 Matrix

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $5 * \\begin{bmatrix} 1 & 0 \\\\ 2 & 9 \\end{bmatrix} =$$\\begin{bmatrix} 5 & 0 \\\\ 10 & 45 \\end{bmatrix}$
    \n", "signature": "(max_matrix_val=10, max_res=100):", "funcdef": "def"}, "mathgenerator.algebra.quadratic_equation": {"fullname": "mathgenerator.algebra.quadratic_equation", "modulename": "mathgenerator.algebra", "qualname": "quadratic_equation", "kind": "function", "doc": "

    Quadratic Equation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What are the zeros of the quadratic equation $22x^2+137x+25=0$${-0.19, -6.04}$
    \n", "signature": "(max_val=100):", "funcdef": "def"}, "mathgenerator.algebra.simple_interest": {"fullname": "mathgenerator.algebra.simple_interest", "modulename": "mathgenerator.algebra", "qualname": "simple_interest", "kind": "function", "doc": "

    Simple Interest

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Simple interest for a principle amount of $7217$ dollars, $3$% rate of interest and for a time period of $10$ years is $=$$2165.1$
    \n", "signature": "(max_principle=10000, max_rate=10, max_time=10):", "funcdef": "def"}, "mathgenerator.algebra.system_of_equations": {"fullname": "mathgenerator.algebra.system_of_equations", "modulename": "mathgenerator.algebra", "qualname": "system_of_equations", "kind": "function", "doc": "

    Solve a System of Equations in R^2

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given $-x + 5y = -28$ and $9x + 2y = 64$, solve for $x$ and $y$.$x = 8$, $y = -4$
    \n", "signature": "(range_x=10, range_y=10, coeff_mult_range=10):", "funcdef": "def"}, "mathgenerator.algebra.vector_cross": {"fullname": "mathgenerator.algebra.vector_cross", "modulename": "mathgenerator.algebra", "qualname": "vector_cross", "kind": "function", "doc": "

    Cross product of 2 vectors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $[-1, -4, 10] \\times [-11, 1, -16] = $$[54, -126, -45]$
    \n", "signature": "(min_val=-20, max_val=20):", "funcdef": "def"}, "mathgenerator.algebra.vector_dot": {"fullname": "mathgenerator.algebra.vector_dot", "modulename": "mathgenerator.algebra", "qualname": "vector_dot", "kind": "function", "doc": "

    Dot product of 2 vectors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $[12, -9, -8]\\cdot[-9, 8, 1]=$$-188$
    \n", "signature": "(min_val=-20, max_val=20):", "funcdef": "def"}, "mathgenerator.algebra.orthogonal_projection": {"fullname": "mathgenerator.algebra.orthogonal_projection", "modulename": "mathgenerator.algebra", "qualname": "orthogonal_projection", "kind": "function", "doc": "

    Orthogonal Projection

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the orthogonal projection of $[2, 3]$ onto $[4, -7]$$[\\frac{-4}{5}, \\frac{7}{5}]$
    \n", "signature": "(min_val=-10, max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math": {"fullname": "mathgenerator.basic_math", "modulename": "mathgenerator.basic_math", "kind": "module", "doc": "

    \n"}, "mathgenerator.basic_math.absolute_difference": {"fullname": "mathgenerator.basic_math.absolute_difference", "modulename": "mathgenerator.basic_math", "qualname": "absolute_difference", "kind": "function", "doc": "

    Absolute difference between two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $|22-34|=$$12$
    \n", "signature": "(max_a=100, max_b=100):", "funcdef": "def"}, "mathgenerator.basic_math.addition": {"fullname": "mathgenerator.basic_math.addition", "modulename": "mathgenerator.basic_math", "qualname": "addition", "kind": "function", "doc": "

    Addition of two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $22+34=$$56$
    \n", "signature": "(max_sum=99, max_addend=50):", "funcdef": "def"}, "mathgenerator.basic_math.compare_fractions": {"fullname": "mathgenerator.basic_math.compare_fractions", "modulename": "mathgenerator.basic_math", "qualname": "compare_fractions", "kind": "function", "doc": "

    Compare Fractions

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Which symbol represents the comparison between $\\frac{1}{2}$ and $\\frac{3}{4}$?$>$
    \n", "signature": "(max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math.cube_root": {"fullname": "mathgenerator.basic_math.cube_root", "modulename": "mathgenerator.basic_math", "qualname": "cube_root", "kind": "function", "doc": "

    Cube Root

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the cube root of: $\\sqrt[3]{125}=$ to 2 decimal places?$5$
    \n", "signature": "(min_no=1, max_no=1000):", "funcdef": "def"}, "mathgenerator.basic_math.divide_fractions": {"fullname": "mathgenerator.basic_math.divide_fractions", "modulename": "mathgenerator.basic_math", "qualname": "divide_fractions", "kind": "function", "doc": "

    Divide Fractions

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\frac{7}{9}\\div\\frac{4}{1}=$$\\frac{7}{36}$
    \n", "signature": "(max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math.division": {"fullname": "mathgenerator.basic_math.division", "modulename": "mathgenerator.basic_math", "qualname": "division", "kind": "function", "doc": "

    Division

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $216\\div24=$$9$
    \n", "signature": "(max_a=25, max_b=25):", "funcdef": "def"}, "mathgenerator.basic_math.exponentiation": {"fullname": "mathgenerator.basic_math.exponentiation", "modulename": "mathgenerator.basic_math", "qualname": "exponentiation", "kind": "function", "doc": "

    Exponentiation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $9^{5}=$$8$
    \n", "signature": "(max_base=20, max_expo=10):", "funcdef": "def"}, "mathgenerator.basic_math.factorial": {"fullname": "mathgenerator.basic_math.factorial", "modulename": "mathgenerator.basic_math", "qualname": "factorial", "kind": "function", "doc": "

    Factorial

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $4! =$$24$
    \n", "signature": "(max_input=6):", "funcdef": "def"}, "mathgenerator.basic_math.fraction_multiplication": {"fullname": "mathgenerator.basic_math.fraction_multiplication", "modulename": "mathgenerator.basic_math", "qualname": "fraction_multiplication", "kind": "function", "doc": "

    Fraction Multiplication

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\frac{3}{10}\\cdot\\frac{6}{7}=$$\\frac{9}{35}$
    \n", "signature": "(max_val=10):", "funcdef": "def"}, "mathgenerator.basic_math.fraction_to_decimal": {"fullname": "mathgenerator.basic_math.fraction_to_decimal", "modulename": "mathgenerator.basic_math", "qualname": "fraction_to_decimal", "kind": "function", "doc": "

    Fraction to Decimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $83\\div80=$$1.04$
    \n", "signature": "(max_res=99, max_divid=99):", "funcdef": "def"}, "mathgenerator.basic_math.greatest_common_divisor": {"fullname": "mathgenerator.basic_math.greatest_common_divisor", "modulename": "mathgenerator.basic_math", "qualname": "greatest_common_divisor", "kind": "function", "doc": "

    Greatest Common Divisor of N Numbers ( GCD / HCF )

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $GCD(488075608, 75348096)=$$8$
    \n", "signature": "(numbers_count=2, max_num=1000):", "funcdef": "def"}, "mathgenerator.basic_math.is_composite": {"fullname": "mathgenerator.basic_math.is_composite", "modulename": "mathgenerator.basic_math", "qualname": "is_composite", "kind": "function", "doc": "

    Is Composite

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Is $171$ composite?Yes
    \n", "signature": "(max_num=250):", "funcdef": "def"}, "mathgenerator.basic_math.is_prime": {"fullname": "mathgenerator.basic_math.is_prime", "modulename": "mathgenerator.basic_math", "qualname": "is_prime", "kind": "function", "doc": "

    Is Prime

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Is $37$ prime?Yes
    \n", "signature": "(max_num=100):", "funcdef": "def"}, "mathgenerator.basic_math.multiplication": {"fullname": "mathgenerator.basic_math.multiplication", "modulename": "mathgenerator.basic_math", "qualname": "multiplication", "kind": "function", "doc": "

    Multiplication

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $10\\cdot9=$$90$
    \n", "signature": "(max_multi=12):", "funcdef": "def"}, "mathgenerator.basic_math.percentage": {"fullname": "mathgenerator.basic_math.percentage", "modulename": "mathgenerator.basic_math", "qualname": "percentage", "kind": "function", "doc": "

    Percentage of a number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is $45$% of $39$?$17.55$
    \n", "signature": "(max_value=99, max_percentage=99):", "funcdef": "def"}, "mathgenerator.basic_math.percentage_difference": {"fullname": "mathgenerator.basic_math.percentage_difference", "modulename": "mathgenerator.basic_math", "qualname": "percentage_difference", "kind": "function", "doc": "

    Percentage difference between two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the percentage difference between $2$ and $10$?$133.33$
    \n", "signature": "(max_value=200, min_value=0):", "funcdef": "def"}, "mathgenerator.basic_math.percentage_error": {"fullname": "mathgenerator.basic_math.percentage_error", "modulename": "mathgenerator.basic_math", "qualname": "percentage_error", "kind": "function", "doc": "

    Percentage error

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the percentage error when observed value equals $32$ and exact value equals $81$.$60.49$%
    \n", "signature": "(max_value=100, min_value=-100):", "funcdef": "def"}, "mathgenerator.basic_math.power_of_powers": {"fullname": "mathgenerator.basic_math.power_of_powers", "modulename": "mathgenerator.basic_math", "qualname": "power_of_powers", "kind": "function", "doc": "

    Power of Powers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Simplify $18^{10^{8}}$$18^{80}$
    \n", "signature": "(max_base=50, max_power=10):", "funcdef": "def"}, "mathgenerator.basic_math.square": {"fullname": "mathgenerator.basic_math.square", "modulename": "mathgenerator.basic_math", "qualname": "square", "kind": "function", "doc": "

    Square

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $17^2=$$289$
    \n", "signature": "(max_square_num=20):", "funcdef": "def"}, "mathgenerator.basic_math.square_root": {"fullname": "mathgenerator.basic_math.square_root", "modulename": "mathgenerator.basic_math", "qualname": "square_root", "kind": "function", "doc": "

    Square Root

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\sqrt{64}=$$8$
    \n", "signature": "(min_no=1, max_no=12):", "funcdef": "def"}, "mathgenerator.basic_math.simplify_square_root": {"fullname": "mathgenerator.basic_math.simplify_square_root", "modulename": "mathgenerator.basic_math", "qualname": "simplify_square_root", "kind": "function", "doc": "

    Simplify Square Root

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\sqrt{63}$$3\\sqrt{7}$
    \n", "signature": "(max_variable=100):", "funcdef": "def"}, "mathgenerator.basic_math.subtraction": {"fullname": "mathgenerator.basic_math.subtraction", "modulename": "mathgenerator.basic_math", "qualname": "subtraction", "kind": "function", "doc": "

    Subtraction of two numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $54-22=$$32$
    \n", "signature": "(max_minuend=99, max_diff=99):", "funcdef": "def"}, "mathgenerator.calculus": {"fullname": "mathgenerator.calculus", "modulename": "mathgenerator.calculus", "kind": "module", "doc": "

    \n"}, "mathgenerator.calculus.definite_integral": {"fullname": "mathgenerator.calculus.definite_integral", "modulename": "mathgenerator.calculus", "qualname": "definite_integral", "kind": "function", "doc": "

    Definite Integral of Quadratic Equation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The definite integral within limits $0$ to $1$ of the equation $28x^2 + 32x + 66 = $$91.33$
    \n", "signature": "(max_coef=100):", "funcdef": "def"}, "mathgenerator.calculus.power_rule_differentiation": {"fullname": "mathgenerator.calculus.power_rule_differentiation", "modulename": "mathgenerator.calculus", "qualname": "power_rule_differentiation", "kind": "function", "doc": "

    Power Rule Differentiation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Differentiate $1x^{5} + 4x^{7} + 4x^{4}$$5x^{4} + 28x^{6} + 16x^{3}$
    \n", "signature": "(max_coef=10, max_exp=10, max_terms=5):", "funcdef": "def"}, "mathgenerator.calculus.power_rule_integration": {"fullname": "mathgenerator.calculus.power_rule_integration", "modulename": "mathgenerator.calculus", "qualname": "power_rule_integration", "kind": "function", "doc": "

    Power Rule Integration

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Integrate $9x^{6} + 2x^{6} + 4x^{3}$$\\frac{9}{6}x^{7} + \\frac{2}{6}x^{7} + \\frac{4}{3}x^{4} + C$
    \n", "signature": "(max_coef=10, max_exp=10, max_terms=5):", "funcdef": "def"}, "mathgenerator.calculus.stationary_points": {"fullname": "mathgenerator.calculus.stationary_points", "modulename": "mathgenerator.calculus", "qualname": "stationary_points", "kind": "function", "doc": "

    Stationary Points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $f(x)=6x^3 + 6x^2 + x + 8$${- \\frac{1}{3} - \\frac{\\sqrt{2}}{6}, - \\frac{1}{3} + \\frac{\\sqrt{2}}{6}}$
    \n", "signature": "(max_exp=3, max_coef=10):", "funcdef": "def"}, "mathgenerator.calculus.trig_differentiation": {"fullname": "mathgenerator.calculus.trig_differentiation", "modulename": "mathgenerator.calculus", "qualname": "trig_differentiation", "kind": "function", "doc": "

    Trigonometric Differentiation

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\frac{d}{dx}(\\csc)=$$-\\csc \\cdot \\cot$
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.computer_science": {"fullname": "mathgenerator.computer_science", "modulename": "mathgenerator.computer_science", "kind": "module", "doc": "

    \n"}, "mathgenerator.computer_science.binary_addition": {"fullname": "mathgenerator.computer_science.binary_addition", "modulename": "mathgenerator.computer_science", "qualname": "binary_addition", "kind": "function", "doc": "

    Binary Addition

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    In binary, calculate: $101 + 110110 = $$111011$
    \n", "signature": "(max_sum=256, max_addend=128):", "funcdef": "def"}, "mathgenerator.computer_science.bcd_to_decimal": {"fullname": "mathgenerator.computer_science.bcd_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "bcd_to_decimal", "kind": "function", "doc": "

    Binary Coded Decimal to Integer

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Integer of Binary Coded Decimal $4 =$$17801$
    \n", "signature": "(max_number=10000):", "funcdef": "def"}, "mathgenerator.computer_science.binary_2s_complement": {"fullname": "mathgenerator.computer_science.binary_2s_complement", "modulename": "mathgenerator.computer_science", "qualname": "binary_2s_complement", "kind": "function", "doc": "

    Binary 2's Complement

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    2's complement of $1011 = $$101$
    \n", "signature": "(maxDigits=10):", "funcdef": "def"}, "mathgenerator.computer_science.binary_complement_1s": {"fullname": "mathgenerator.computer_science.binary_complement_1s", "modulename": "mathgenerator.computer_science", "qualname": "binary_complement_1s", "kind": "function", "doc": "

    Binary Complement 1s

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $1111001 = $$0000110$
    \n", "signature": "(maxDigits=10):", "funcdef": "def"}, "mathgenerator.computer_science.binary_to_decimal": {"fullname": "mathgenerator.computer_science.binary_to_decimal", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_decimal", "kind": "function", "doc": "

    Binary to Decimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $000110$$6$
    \n", "signature": "(max_dig=10):", "funcdef": "def"}, "mathgenerator.computer_science.binary_to_hex": {"fullname": "mathgenerator.computer_science.binary_to_hex", "modulename": "mathgenerator.computer_science", "qualname": "binary_to_hex", "kind": "function", "doc": "

    Binary to Hexidecimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $010101$$0x15$
    \n", "signature": "(max_dig=10):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_bcd": {"fullname": "mathgenerator.computer_science.decimal_to_bcd", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_bcd", "kind": "function", "doc": "

    Decimal to Binary Coded Decimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    BCD of Decimal Number $6575 = $$191015$
    \n", "signature": "(max_number=10000):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_binary": {"fullname": "mathgenerator.computer_science.decimal_to_binary", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_binary", "kind": "function", "doc": "

    Decimal to Binary

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Binary of $4 = $$100$
    \n", "signature": "(max_dec=99):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_hexadeci": {"fullname": "mathgenerator.computer_science.decimal_to_hexadeci", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_hexadeci", "kind": "function", "doc": "

    Decimal to Hexadecimal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Hexadecimal of $410 = $$0x19a$
    \n", "signature": "(max_dec=1000):", "funcdef": "def"}, "mathgenerator.computer_science.decimal_to_octal": {"fullname": "mathgenerator.computer_science.decimal_to_octal", "modulename": "mathgenerator.computer_science", "qualname": "decimal_to_octal", "kind": "function", "doc": "

    Decimal to Octal

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The decimal number $3698$ in octal is:$0o7162$
    \n", "signature": "(max_decimal=4096):", "funcdef": "def"}, "mathgenerator.computer_science.fibonacci_series": {"fullname": "mathgenerator.computer_science.fibonacci_series", "modulename": "mathgenerator.computer_science", "qualname": "fibonacci_series", "kind": "function", "doc": "

    Fibonacci Series

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The Fibonacci Series of the first ${n}$ numbers is ?$0, 1, 1, 2, 3, 5, 8, 13, 21$
    \n", "signature": "(min_no=1):", "funcdef": "def"}, "mathgenerator.computer_science.modulo_division": {"fullname": "mathgenerator.computer_science.modulo_division", "modulename": "mathgenerator.computer_science", "qualname": "modulo_division", "kind": "function", "doc": "

    Modulo Division

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $43$ % $33 = $$10$
    \n", "signature": "(max_res=99, max_modulo=99):", "funcdef": "def"}, "mathgenerator.computer_science.nth_fibonacci_number": {"fullname": "mathgenerator.computer_science.nth_fibonacci_number", "modulename": "mathgenerator.computer_science", "qualname": "nth_fibonacci_number", "kind": "function", "doc": "

    nth Fibonacci number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the 85th Fibonacci number?$259695496911123328$
    \n", "signature": "(max_n=100):", "funcdef": "def"}, "mathgenerator.computer_science.nth_tribonacci_number": {"fullname": "mathgenerator.computer_science.nth_tribonacci_number", "modulename": "mathgenerator.computer_science", "qualname": "nth_tribonacci_number", "kind": "function", "doc": "

    nth Tribonacci number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the 14th Tribonacci number?$504$
    \n", "signature": "(min_length=1, max_length=80):", "funcdef": "def"}, "mathgenerator.computer_science.tribonacci_series": {"fullname": "mathgenerator.computer_science.tribonacci_series", "modulename": "mathgenerator.computer_science", "qualname": "tribonacci_series", "kind": "function", "doc": "

    Fibonacci Series

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The Tribonacci Series of the first $8$ numbers is ?$0, 0, 1, 1, 2, 4, 7, 13$
    \n", "signature": "(min_length=1, max_length=80):", "funcdef": "def"}, "mathgenerator.geometry": {"fullname": "mathgenerator.geometry", "modulename": "mathgenerator.geometry", "kind": "module", "doc": "

    \n"}, "mathgenerator.geometry.angle_btw_vectors": {"fullname": "mathgenerator.geometry.angle_btw_vectors", "modulename": "mathgenerator.geometry", "qualname": "angle_btw_vectors", "kind": "function", "doc": "

    Angle between 2 vectors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    angle between the vectors $[363.84, 195.54, 997.08, 39.26, 60.14, 722.7, 888.57, 713.15, 436.22, 712.23, 349.23, 595.91, 191.8, 824.58, 861.56, 122.73, 815.14, 700.68, 506.5]$ and $[760.85, 934.67, 513.37, 796.93, 809.97, 423.54, 162.69, 758.96, 133.42, 478.14, 771.84, 824.88, 483.07, 134.41, 954.41, 893.42, 191.01, 453.97, 648.59]$ is:$0.81$ radians
    \n", "signature": "(max_elt_amt=20):", "funcdef": "def"}, "mathgenerator.geometry.angle_regular_polygon": {"fullname": "mathgenerator.geometry.angle_regular_polygon", "modulename": "mathgenerator.geometry", "qualname": "angle_regular_polygon", "kind": "function", "doc": "

    Angle of a Regular Polygon

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the angle of a regular polygon with $8$ sides$135.0$
    \n", "signature": "(min_val=3, max_val=20):", "funcdef": "def"}, "mathgenerator.geometry.arc_length": {"fullname": "mathgenerator.geometry.arc_length", "modulename": "mathgenerator.geometry", "qualname": "arc_length", "kind": "function", "doc": "

    Arc length of Angle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given radius, $44$ and angle, $184$. Find the arc length of the angle.Arc length of the angle $= 141.30186$
    \n", "signature": "(max_radius=49, max_angle=359):", "funcdef": "def"}, "mathgenerator.geometry.area_of_circle": {"fullname": "mathgenerator.geometry.area_of_circle", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle", "kind": "function", "doc": "

    Area of Circle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of circle with radius $29=$$2642.08$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.geometry.area_of_circle_given_center_and_point": {"fullname": "mathgenerator.geometry.area_of_circle_given_center_and_point", "modulename": "mathgenerator.geometry", "qualname": "area_of_circle_given_center_and_point", "kind": "function", "doc": "

    Area of Circle given center and a point on circle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of circle with center $(7,-6)$ and passing through $(1.0, -6.0)$ is$113.1$
    \n", "signature": "(max_coordinate=10, max_radius=10):", "funcdef": "def"}, "mathgenerator.geometry.area_of_trapezoid": {"fullname": "mathgenerator.geometry.area_of_trapezoid", "modulename": "mathgenerator.geometry", "qualname": "area_of_trapezoid", "kind": "function", "doc": "

    Area of Trapezoid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of trapezoid with height $12$ and base lengths: $3, 7, = $$60$
    \n", "signature": "(max_len=20):", "funcdef": "def"}, "mathgenerator.geometry.area_of_triangle": {"fullname": "mathgenerator.geometry.area_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "area_of_triangle", "kind": "function", "doc": "

    Area of Triangle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Area of triangle with side lengths: $8, 1, 8 = $$3.99$
    \n", "signature": "(max_a=20, max_b=20):", "funcdef": "def"}, "mathgenerator.geometry.basic_trigonometry": {"fullname": "mathgenerator.geometry.basic_trigonometry", "modulename": "mathgenerator.geometry", "qualname": "basic_trigonometry", "kind": "function", "doc": "

    Trigonometric Values

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $\\sin(30) = $$\\frac{1}{2}$
    \n", "signature": "(angles=[0, 30, 45, 60, 90], functions=['sin', 'cos', 'tan']):", "funcdef": "def"}, "mathgenerator.geometry.circumference": {"fullname": "mathgenerator.geometry.circumference", "modulename": "mathgenerator.geometry", "qualname": "circumference", "kind": "function", "doc": "

    Circumference of Circle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Circumference of circle with radius $56 = $$351.86$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.geometry.complementary_and_supplementary_angle": {"fullname": "mathgenerator.geometry.complementary_and_supplementary_angle", "modulename": "mathgenerator.geometry", "qualname": "complementary_and_supplementary_angle", "kind": "function", "doc": "

    Complementary and Supplementary Angle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The complementary angle of $15 =$$75$
    \n", "signature": "(max_supp=180, max_comp=90):", "funcdef": "def"}, "mathgenerator.geometry.curved_surface_area_cylinder": {"fullname": "mathgenerator.geometry.curved_surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "curved_surface_area_cylinder", "kind": "function", "doc": "

    Curved surface area of a cylinder

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the curved surface area of a cylinder of radius, $44$ and height, $92$?$25434.33$
    \n", "signature": "(max_radius=49, max_height=99):", "funcdef": "def"}, "mathgenerator.geometry.degree_to_rad": {"fullname": "mathgenerator.geometry.degree_to_rad", "modulename": "mathgenerator.geometry", "qualname": "degree_to_rad", "kind": "function", "doc": "

    Degrees to Radians

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Angle $113$ degrees in radians is:$1.97$
    \n", "signature": "(max_deg=360):", "funcdef": "def"}, "mathgenerator.geometry.equation_of_line_from_two_points": {"fullname": "mathgenerator.geometry.equation_of_line_from_two_points", "modulename": "mathgenerator.geometry", "qualname": "equation_of_line_from_two_points", "kind": "function", "doc": "

    Equation of line from two points

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the equation of the line between points $(13,9)$ and $(6,-19)$ in slope-intercept form?$y = 4x -43$
    \n", "signature": "(max_coordinate=20, min_coordinate=-20):", "funcdef": "def"}, "mathgenerator.geometry.fourth_angle_of_quadrilateral": {"fullname": "mathgenerator.geometry.fourth_angle_of_quadrilateral", "modulename": "mathgenerator.geometry", "qualname": "fourth_angle_of_quadrilateral", "kind": "function", "doc": "

    Fourth Angle of Quadrilateral

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Fourth angle of quadrilateral with angles $162 , 43, 78 =$$77$
    \n", "signature": "(max_angle=180):", "funcdef": "def"}, "mathgenerator.geometry.perimeter_of_polygons": {"fullname": "mathgenerator.geometry.perimeter_of_polygons", "modulename": "mathgenerator.geometry", "qualname": "perimeter_of_polygons", "kind": "function", "doc": "

    Perimeter of Polygons

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The perimeter of a $4$ sided polygon with lengths of $30, 105, 78, 106$cm is:$319$
    \n", "signature": "(max_sides=12, max_length=120):", "funcdef": "def"}, "mathgenerator.geometry.pythagorean_theorem": {"fullname": "mathgenerator.geometry.pythagorean_theorem", "modulename": "mathgenerator.geometry", "qualname": "pythagorean_theorem", "kind": "function", "doc": "

    Pythagorean Theorem

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the hypotenuse of a right triangle given the other two sides have lengths $9$ and $10$?$13.45$
    \n", "signature": "(max_length=20):", "funcdef": "def"}, "mathgenerator.geometry.radian_to_deg": {"fullname": "mathgenerator.geometry.radian_to_deg", "modulename": "mathgenerator.geometry", "qualname": "radian_to_deg", "kind": "function", "doc": "

    Radians to Degrees

    \n", "signature": "(max_rad=6.28):", "funcdef": "def"}, "mathgenerator.geometry.sector_area": {"fullname": "mathgenerator.geometry.sector_area", "modulename": "mathgenerator.geometry", "qualname": "sector_area", "kind": "function", "doc": "

    Area of a Sector

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the area of a sector with radius $42$ and angle $83$ degrees?$1277.69$
    \n", "signature": "(max_radius=49, max_angle=359):", "funcdef": "def"}, "mathgenerator.geometry.sum_of_polygon_angles": {"fullname": "mathgenerator.geometry.sum_of_polygon_angles", "modulename": "mathgenerator.geometry", "qualname": "sum_of_polygon_angles", "kind": "function", "doc": "

    Sum of Angles of Polygon

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the sum of interior angles of a polygon with $8$ sides?$1080$
    \n", "signature": "(max_sides=12):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cone": {"fullname": "mathgenerator.geometry.surface_area_cone", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cone", "kind": "function", "doc": "

    Surface area of a cone

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cone with height $= 26m$ and radius $= 6m$ is$616 m^2$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cube": {"fullname": "mathgenerator.geometry.surface_area_cube", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cube", "kind": "function", "doc": "

    Surface area of a cube

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cube with side $= 6m$ is$216 m^2$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cuboid": {"fullname": "mathgenerator.geometry.surface_area_cuboid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cuboid", "kind": "function", "doc": "

    Surface area of a cuboid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cuboid with sides of lengths: $11m, 20m, 8m$ is$936 m^2$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_cylinder": {"fullname": "mathgenerator.geometry.surface_area_cylinder", "modulename": "mathgenerator.geometry", "qualname": "surface_area_cylinder", "kind": "function", "doc": "

    Surface area of a cylinder

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of cylinder with height $= 26m$ and radius $= 15m$ is$3864 m^2$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_pyramid": {"fullname": "mathgenerator.geometry.surface_area_pyramid", "modulename": "mathgenerator.geometry", "qualname": "surface_area_pyramid", "kind": "function", "doc": "

    Surface area of a pyramid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of pyramid with base length $= 30m$, base width $= 40m$, and height $= 25m$ is$2400 m^2$
    \n", "signature": "(unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.surface_area_sphere": {"fullname": "mathgenerator.geometry.surface_area_sphere", "modulename": "mathgenerator.geometry", "qualname": "surface_area_sphere", "kind": "function", "doc": "

    Surface area of a sphere

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Surface area of a sphere with radius $= 8m$ is$804.25 m^2$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.third_angle_of_triangle": {"fullname": "mathgenerator.geometry.third_angle_of_triangle", "modulename": "mathgenerator.geometry", "qualname": "third_angle_of_triangle", "kind": "function", "doc": "

    Third Angle of Triangle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Third angle of triangle with angles $10$ and $22 =$$148$
    \n", "signature": "(max_angle=89):", "funcdef": "def"}, "mathgenerator.geometry.valid_triangle": {"fullname": "mathgenerator.geometry.valid_triangle", "modulename": "mathgenerator.geometry", "qualname": "valid_triangle", "kind": "function", "doc": "

    Valid Triangle

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Does triangel with sides $10, 31$ and $14$ exist?No
    \n", "signature": "(max_side_length=50):", "funcdef": "def"}, "mathgenerator.geometry.volume_cone": {"fullname": "mathgenerator.geometry.volume_cone", "modulename": "mathgenerator.geometry", "qualname": "volume_cone", "kind": "function", "doc": "

    Volume of a cone

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of cone with height $= 44m$ and radius $= 11m$ is$5575 m^3$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cube": {"fullname": "mathgenerator.geometry.volume_cube", "modulename": "mathgenerator.geometry", "qualname": "volume_cube", "kind": "function", "doc": "

    Volume of a cube

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of a cube with a side length of $19m$ is$6859 m^3$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cuboid": {"fullname": "mathgenerator.geometry.volume_cuboid", "modulename": "mathgenerator.geometry", "qualname": "volume_cuboid", "kind": "function", "doc": "

    Volume of a cuboid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of cuboid with sides = $17m, 11m, 13m$ is$2431 m^3$
    \n", "signature": "(max_side=20, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cylinder": {"fullname": "mathgenerator.geometry.volume_cylinder", "modulename": "mathgenerator.geometry", "qualname": "volume_cylinder", "kind": "function", "doc": "

    Volume of a cylinder

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of cylinder with height $= 3m$ and radius $= 10m$ is$942 m^3$
    \n", "signature": "(max_radius=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_cone_frustum": {"fullname": "mathgenerator.geometry.volume_cone_frustum", "modulename": "mathgenerator.geometry", "qualname": "volume_cone_frustum", "kind": "function", "doc": "

    Volume of the frustum of a cone

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of frustum with height $= 30m$ and $r1 = 20m$ is and $r2 = 8m$ is$19603.54 m^3$
    \n", "signature": "(max_r1=20, max_r2=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_hemisphere": {"fullname": "mathgenerator.geometry.volume_hemisphere", "modulename": "mathgenerator.geometry", "qualname": "volume_hemisphere", "kind": "function", "doc": "

    Volume of a hemisphere

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of hemisphere with radius $32m =$$68629.14 m^3$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.geometry.volume_pyramid": {"fullname": "mathgenerator.geometry.volume_pyramid", "modulename": "mathgenerator.geometry", "qualname": "volume_pyramid", "kind": "function", "doc": "

    Volume of a pyramid

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of pyramid with base length $= 7 m$, base width $= 18 m$ and height $= 42 m$ is$1764.0 m^3$
    \n", "signature": "(max_length=20, max_width=20, max_height=50, unit='m'):", "funcdef": "def"}, "mathgenerator.geometry.volume_sphere": {"fullname": "mathgenerator.geometry.volume_sphere", "modulename": "mathgenerator.geometry", "qualname": "volume_sphere", "kind": "function", "doc": "

    Volume of a sphere

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Volume of sphere with radius $30 m = $$113097.36 m^3$
    \n", "signature": "(max_radius=100):", "funcdef": "def"}, "mathgenerator.misc": {"fullname": "mathgenerator.misc", "modulename": "mathgenerator.misc", "kind": "module", "doc": "

    \n"}, "mathgenerator.misc.arithmetic_progression_sum": {"fullname": "mathgenerator.misc.arithmetic_progression_sum", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_sum", "kind": "function", "doc": "

    Arithmetic Progression Sum

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the sum of first $44$ terms of the AP series: $49, 145, 241 ... $$92972.0$
    \n", "signature": "(max_d=100, max_a=100, max_n=100):", "funcdef": "def"}, "mathgenerator.misc.arithmetic_progression_term": {"fullname": "mathgenerator.misc.arithmetic_progression_term", "modulename": "mathgenerator.misc", "qualname": "arithmetic_progression_term", "kind": "function", "doc": "

    Arithmetic Progression Term

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find term number $12$ of the AP series: $-54, 24, 102 ... $$804$
    \n", "signature": "(max_d=100, max_a=100, max_n=100):", "funcdef": "def"}, "mathgenerator.misc.base_conversion": {"fullname": "mathgenerator.misc.base_conversion", "modulename": "mathgenerator.misc", "qualname": "base_conversion", "kind": "function", "doc": "

    Base Conversion

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Convert $45204$ from base $10$ to base $4$$23002110$
    \n", "signature": "(max_num=60000, max_base=16):", "funcdef": "def"}, "mathgenerator.misc.binomial_distribution": {"fullname": "mathgenerator.misc.binomial_distribution", "modulename": "mathgenerator.misc", "qualname": "binomial_distribution", "kind": "function", "doc": "

    Binomial distribution

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    A manufacturer of metal pistons finds that, on average, $30.56$% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of $20$ pistons will contain no more than $2$ rejected pistons?$3.17$
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.misc.celsius_to_fahrenheit": {"fullname": "mathgenerator.misc.celsius_to_fahrenheit", "modulename": "mathgenerator.misc", "qualname": "celsius_to_fahrenheit", "kind": "function", "doc": "

    Celsius to Fahrenheit

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Convert $-46$ degrees Celsius to degrees Fahrenheit$-50.8$
    \n", "signature": "(max_temp=100):", "funcdef": "def"}, "mathgenerator.misc.common_factors": {"fullname": "mathgenerator.misc.common_factors", "modulename": "mathgenerator.misc", "qualname": "common_factors", "kind": "function", "doc": "

    Common Factors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Common Factors of $100$ and $44 = $$[1, 2, 4]$
    \n", "signature": "(max_val=100):", "funcdef": "def"}, "mathgenerator.misc.complex_to_polar": {"fullname": "mathgenerator.misc.complex_to_polar", "modulename": "mathgenerator.misc", "qualname": "complex_to_polar", "kind": "function", "doc": "

    Complex to polar form

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    $19.42(-19.0\\theta + i-4.0\\theta)$$-2.93$
    \n", "signature": "(min_real_imaginary_num=-20, max_real_imaginary_num=20):", "funcdef": "def"}, "mathgenerator.misc.decimal_to_roman_numerals": {"fullname": "mathgenerator.misc.decimal_to_roman_numerals", "modulename": "mathgenerator.misc", "qualname": "decimal_to_roman_numerals", "kind": "function", "doc": "

    Decimal to Roman Numerals

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The number $92$ in roman numerals is:$XCII$
    \n", "signature": "(max_decimal=3999):", "funcdef": "def"}, "mathgenerator.misc.euclidian_norm": {"fullname": "mathgenerator.misc.euclidian_norm", "modulename": "mathgenerator.misc", "qualname": "euclidian_norm", "kind": "function", "doc": "

    Euclidian norm or L2 norm of a vector

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Euclidian norm or L2 norm of the vector $[659.9225071540442, 243.40887829281564, 128.79950053874424, 263.19226900031344]$ is:$761.97$
    \n", "signature": "(maxEltAmt=20):", "funcdef": "def"}, "mathgenerator.misc.factors": {"fullname": "mathgenerator.misc.factors", "modulename": "mathgenerator.misc", "qualname": "factors", "kind": "function", "doc": "

    Factors of a number

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Factors of $176 = $$[1, 2, 4, 8, 11, 16, 22, 44, 88, 176]$
    \n", "signature": "(max_val=1000):", "funcdef": "def"}, "mathgenerator.misc.geometric_mean": {"fullname": "mathgenerator.misc.geometric_mean", "modulename": "mathgenerator.misc", "qualname": "geometric_mean", "kind": "function", "doc": "

    Geometric Mean of N Numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Geometric mean of $3$ numbers $[72, 21, 87] = $$50.86$
    \n", "signature": "(max_value=100, max_count=4):", "funcdef": "def"}, "mathgenerator.misc.geometric_progression": {"fullname": "mathgenerator.misc.geometric_progression", "modulename": "mathgenerator.misc", "qualname": "geometric_progression", "kind": "function", "doc": "

    Geometric Progression

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    For the given GP $[11, 44, 176, 704, 2816, 11264]$. Find the value of a common ratio, 7th term value, sum upto 10th termThe value of a is $11$, common ratio is $4$ , 7th term is $45056$, sum upto 10th term is $3844775.0$
    \n", "signature": "(number_values=6, min_value=2, max_value=12, n_term=7, sum_term=5):", "funcdef": "def"}, "mathgenerator.misc.harmonic_mean": {"fullname": "mathgenerator.misc.harmonic_mean", "modulename": "mathgenerator.misc", "qualname": "harmonic_mean", "kind": "function", "doc": "

    Harmonic Mean of N Numbers

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Harmonic mean of $4$ numbers $52, 56, 25, 57 = $$602.33$
    \n", "signature": "(max_value=100, max_count=4):", "funcdef": "def"}, "mathgenerator.misc.is_leap_year": {"fullname": "mathgenerator.misc.is_leap_year", "modulename": "mathgenerator.misc", "qualname": "is_leap_year", "kind": "function", "doc": "

    Is Leap Year or Not

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Is $2000$ a leap year?$2000$ is a leap year
    \n", "signature": "(minNumber=1900, max_number=2099):", "funcdef": "def"}, "mathgenerator.misc.lcm": {"fullname": "mathgenerator.misc.lcm", "modulename": "mathgenerator.misc", "qualname": "lcm", "kind": "function", "doc": "

    LCM (Least Common Multiple)

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    LCM of $3$ and $18 = $$18$
    \n", "signature": "(max_val=20):", "funcdef": "def"}, "mathgenerator.misc.minutes_to_hours": {"fullname": "mathgenerator.misc.minutes_to_hours", "modulename": "mathgenerator.misc", "qualname": "minutes_to_hours", "kind": "function", "doc": "

    Convert minutes to hours and minutes

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Convert $836$ minutes to hours & minutes$13$ hours and $56$ minutes
    \n", "signature": "(max_minutes=999):", "funcdef": "def"}, "mathgenerator.misc.prime_factors": {"fullname": "mathgenerator.misc.prime_factors", "modulename": "mathgenerator.misc", "qualname": "prime_factors", "kind": "function", "doc": "

    Prime Factors

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find prime factors of $30$$2, 3, 5$
    \n", "signature": "(min_val=1, max_val=200):", "funcdef": "def"}, "mathgenerator.misc.product_of_scientific_notations": {"fullname": "mathgenerator.misc.product_of_scientific_notations", "modulename": "mathgenerator.misc", "qualname": "product_of_scientific_notations", "kind": "function", "doc": "

    Product of scientific notations

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Product of scientific notations $5.11 \\times 10^{67}$ and $3.64 \\times 10^{-59} = $$1.86 \\times 10^{9}$
    \n", "signature": "(min_exp_val=-100, max_exp_val=100):", "funcdef": "def"}, "mathgenerator.misc.profit_loss_percent": {"fullname": "mathgenerator.misc.profit_loss_percent", "modulename": "mathgenerator.misc", "qualname": "profit_loss_percent", "kind": "function", "doc": "

    Profit or Loss Percent

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Loss percent when $CP = 751$ and $SP = 290$ is:$61.38$
    \n", "signature": "(max_cp=1000, max_sp=1000):", "funcdef": "def"}, "mathgenerator.misc.quotient_of_power_same_base": {"fullname": "mathgenerator.misc.quotient_of_power_same_base", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_base", "kind": "function", "doc": "

    Quotient of Powers with Same Base

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The Quotient of $5^{6}$ and $5^{8} = 5^{6-8} = 5^{-2}$$0.04$
    \n", "signature": "(max_base=50, max_power=10):", "funcdef": "def"}, "mathgenerator.misc.quotient_of_power_same_power": {"fullname": "mathgenerator.misc.quotient_of_power_same_power", "modulename": "mathgenerator.misc", "qualname": "quotient_of_power_same_power", "kind": "function", "doc": "

    Quotient of Powers with Same Power

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The quotient of $19^{8}$ and $10^{8} = (19/10)^8 = 1.9^{8}$$169.84$
    \n", "signature": "(max_base=50, max_power=10):", "funcdef": "def"}, "mathgenerator.misc.set_operation": {"fullname": "mathgenerator.misc.set_operation", "modulename": "mathgenerator.misc", "qualname": "set_operation", "kind": "function", "doc": "

    Union, Intersection, Difference of Two Sets

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given the two sets $a={1, 2, 4, 5}$, $b={8, 1, 2}$. Find the Union, intersection, $a-b$, $b-a$, and symmetric differenceUnion is ${1, 2, 4, 5, 8}$. Intersection is ${1, 2}$, $a-b$ is ${4, 5}$, $b-a$ is ${8}$. Symmetric difference is ${4, 5, 8}$.
    \n", "signature": "(min_size=3, max_size=7):", "funcdef": "def"}, "mathgenerator.misc.signum_function": {"fullname": "mathgenerator.misc.signum_function", "modulename": "mathgenerator.misc", "qualname": "signum_function", "kind": "function", "doc": "

    Signum Function

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Signum of $-229$ is =$-1$
    \n", "signature": "(min=-999, max=999):", "funcdef": "def"}, "mathgenerator.misc.surds_comparison": {"fullname": "mathgenerator.misc.surds_comparison", "modulename": "mathgenerator.misc", "qualname": "surds_comparison", "kind": "function", "doc": "

    Comparing Surds

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Fill in the blanks $42^{\\frac{1}{2}}$ _ $45^{\\frac{1}{5}}$$>$
    \n", "signature": "(max_value=100, max_root=10):", "funcdef": "def"}, "mathgenerator.misc.velocity_of_object": {"fullname": "mathgenerator.misc.velocity_of_object", "modulename": "mathgenerator.misc", "qualname": "velocity_of_object", "kind": "function", "doc": "

    Velocity of object

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    An object travels at uniform velocity a distance of $100 m$ in $4$ seconds. What is the velocity of the car?$25 m/s$
    \n", "signature": "(max_displacement=1000, max_time=100):", "funcdef": "def"}, "mathgenerator.physics": {"fullname": "mathgenerator.physics", "modulename": "mathgenerator.physics", "kind": "module", "doc": "

    \n"}, "mathgenerator.physics.kinetic_energy": {"fullname": "mathgenerator.physics.kinetic_energy", "modulename": "mathgenerator.physics", "qualname": "kinetic_energy", "kind": "function", "doc": "

    Kinetic Energy calculation using Ek = 0.5 * m * v^2

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    What is the kinetic energy of an object of mass $5 kg$ and velocity $10 m/s$$250 J$
    \n", "signature": "(max_mass=1000, max_vel=100):", "funcdef": "def"}, "mathgenerator.physics.potential_dividers": {"fullname": "mathgenerator.physics.potential_dividers", "modulename": "mathgenerator.physics", "qualname": "potential_dividers", "kind": "function", "doc": "

    Potential Divider question using Vout = (Vin * R2) / (R2 + R1)

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    In a Potential Divider, if resistors R1 and R2 have resistances of $100 \\Omega$ and $50 \\Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2?$4 V$
    \n", "signature": "(max_vin=50, max_resistance=500):", "funcdef": "def"}, "mathgenerator.physics.resistivity": {"fullname": "mathgenerator.physics.resistivity", "modulename": "mathgenerator.physics", "qualname": "resistivity", "kind": "function", "doc": "

    Calculate the Resistivity using the equation R = (pL)/A, where R = Resistance, L = length of wire, p = resistivity and A = cross sectional area of wire

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    A wire has resistance $30 m\\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire$6.14e-07 \\Omega m$
    \n", "signature": "(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1):", "funcdef": "def"}, "mathgenerator.physics.fringe_spacing": {"fullname": "mathgenerator.physics.fringe_spacing", "modulename": "mathgenerator.physics", "qualname": "fringe_spacing", "kind": "function", "doc": "

    Calculate the fringe spacing in a double slit experiment with w=(\u03bbD)/s

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes.Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$
    \n", "signature": "(max_screen_distance=30, max_slit_spacing_mm=100):", "funcdef": "def"}, "mathgenerator.statistics": {"fullname": "mathgenerator.statistics", "modulename": "mathgenerator.statistics", "kind": "module", "doc": "

    \n"}, "mathgenerator.statistics.combinations": {"fullname": "mathgenerator.statistics.combinations", "modulename": "mathgenerator.statistics", "qualname": "combinations", "kind": "function", "doc": "

    Combinations of Objects

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the number of combinations from $19$ objects picked $6$ at a time.$27132$
    \n", "signature": "(max_lengthgth=20):", "funcdef": "def"}, "mathgenerator.statistics.conditional_probability": {"fullname": "mathgenerator.statistics.conditional_probability", "modulename": "mathgenerator.statistics", "qualname": "conditional_probability", "kind": "function", "doc": "

    Conditional Probability

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Someone tested positive for a nasty disease which only $1.18$% of the population have. Test sensitivity (true positive) is equal to $SN=98.73$% whereas test specificity (true negative) $SP=99.99$%. What is the probability that this guy really has that disease?$99.16$%
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.statistics.confidence_interval": {"fullname": "mathgenerator.statistics.confidence_interval", "modulename": "mathgenerator.statistics", "qualname": "confidence_interval", "kind": "function", "doc": "

    Confidence interval For sample S

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    The confidence interval for sample $[234, 223, 210, 203, 258, 299, 281, 208, 278, 252, 295, 245, 280, 235, 219, 297, 214, 267, 212, 256, 232, 221]$ with $99$% confidence is$(263.31, 229.33)$
    \n", "signature": "():", "funcdef": "def"}, "mathgenerator.statistics.data_summary": {"fullname": "mathgenerator.statistics.data_summary", "modulename": "mathgenerator.statistics", "qualname": "data_summary", "kind": "function", "doc": "

    Mean, Standard Deviation and Variance

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Find the mean,standard deviation and variance for the data $9, 29, 46, 27, 46, 15, 10, 44, 19, 33, 38, 7, 34, 28, 8$The Mean is $26.2$, Standard Deviation is $186.29$, Variance is $13.65$
    \n", "signature": "(number_values=15, min_val=5, max_val=50):", "funcdef": "def"}, "mathgenerator.statistics.dice_sum_probability": {"fullname": "mathgenerator.statistics.dice_sum_probability", "modulename": "mathgenerator.statistics", "qualname": "dice_sum_probability", "kind": "function", "doc": "

    Probability of a certain sum appearing on faces of dice

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    If $2$ dice are rolled at the same time, the probability of getting a sum of $5 =$$\\frac{4}{36}$
    \n", "signature": "(max_dice=3):", "funcdef": "def"}, "mathgenerator.statistics.mean_median": {"fullname": "mathgenerator.statistics.mean_median", "modulename": "mathgenerator.statistics", "qualname": "mean_median", "kind": "function", "doc": "

    Mean and Median

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Given the series of numbers $[4, 19, 21, 22, 43, 44, 60, 81, 87, 92]$. Find the arithmatic mean and median of the seriesArithmetic mean of the series is $47.3$ and arithmetic median of this series is $43.5$
    \n", "signature": "(max_length=10):", "funcdef": "def"}, "mathgenerator.statistics.permutation": {"fullname": "mathgenerator.statistics.permutation", "modulename": "mathgenerator.statistics", "qualname": "permutation", "kind": "function", "doc": "

    Permutations

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n
    Ex. ProblemEx. Solution
    Number of Permutations from $18$ objects picked $5$ at a time is:$1028160$
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{"mathgenerator.algebra.quadratic_equation": {"tf": 1}}, "df": 1}}}}}}}}, "pipeline": ["trimmer"], "_isPrebuiltIndex": true}; // mirrored in build-search-index.js (part 1) // Also split on html tags. this is a cheap heuristic, but good enough. diff --git a/mathgenerator/_gen_list.py b/mathgenerator/_gen_list.py index cd17914..521d287 100644 --- a/mathgenerator/_gen_list.py +++ b/mathgenerator/_gen_list.py @@ -136,4 +136,5 @@ gen_list = [ ("kinetic_energy", "physics"), ("potential_dividers", "physics"), ("resistivity", "physics"), + ("fringe_spacing", "physics"), ] diff --git a/mathgenerator/physics.py b/mathgenerator/physics.py index 8f46e76..8ce2537 100644 --- a/mathgenerator/physics.py +++ b/mathgenerator/physics.py @@ -1,6 +1,7 @@ import random import math +# Generic def kinetic_energy(max_mass=1000, max_vel=100): r"""Kinetic Energy calculation using Ek = 0.5 * m * v^2 @@ -17,12 +18,14 @@ def kinetic_energy(max_mass=1000, max_vel=100): solution = f'${kinetic_energy} J$' return problem, solution + +# Electricity def potential_dividers(max_vin=50, max_resistance=500): r"""Potential Divider question using Vout = (Vin * R2) / (R2 + R1) | Ex. Problem | Ex. Solution | | --- | --- | - | In a Potential Divider, if resistors R1 and R2 have resistances of $100 Ω$ and $50 Ω$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ | + | In a Potential Divider, if resistors R1 and R2 have resistances of $100 \Omega$ and $50 \Omega$ respectively, and the cell has $12 V$ What is the output potential difference across R2? | $4 V$ | """ ''' This is what a potential divider circuit looks like: @@ -37,7 +40,7 @@ def potential_dividers(max_vin=50, max_resistance=500): r2 = random.randint(0, max_resistance) # Resistance of R2 vout = round((vin * r2) / (r1 + r2),2) # Voltage output across R2 - problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} Ω$ and ${r2} Ω$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?" + problem = f"In a Potential Divider, if resistors R1 and R2 have resistances of ${r1} \\Omega$ and ${r2} \\Omega$ respectively, and the cell has ${vin} V$ What is the output potential difference across R2?" solution = f"${vout} V$" return problem, solution @@ -46,7 +49,7 @@ def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1): | Ex. Problem | Ex. Solution | | --- | --- | - | A wire has resistance $30 mΩ$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 Ωm$ | + | A wire has resistance $30 m\Omega$ when it is $83.64 cm$ long with a diameter of $4.67 mm$. Calculate the resistivity of the wire | $6.14e-07 \Omega m$ | """ # This question requires a lot of unit conversions and calculating the area of a circle from diameter diameter_mm = round(random.uniform(0, max_diameter_mm),2) # Random diameter in mm @@ -56,10 +59,29 @@ def resistivity(max_diameter_mm=5, max_length_cm=100, max_resistance=0.1): resistivity = (resistance * cross_sectional_area) / (length_cm / 100) - problem = f"A wire has resistance ${resistance*1000} mΩ$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire" - solution = f"${resistivity:.2e} Ωm$" + problem = f"A wire has resistance ${resistance*1000} m\\Omega$ when it is ${length_cm} cm$ long with a diameter of ${diameter_mm} mm$. Calculate the resistivity of the wire" + solution = f"${resistivity:.2e} \\Omega m$" return problem, solution +# Waves +def fringe_spacing(max_screen_distance=30, max_slit_spacing_mm=100): + r"""Calculate the fringe spacing in a double slit experiment with w=(λD)/s + | Ex. Problem | Ex. Solution | + | --- | --- | + | A laser with a wavelength of $450nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is $12m$ from the slits and the slits are $0.30mm$ apart. Calculate the spacing between the bright fringes. | Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of $0.018m$ | + """ + wavelength_nm = random.randint(380,750) # Random wavelength between violet and red (nm) + screen_distance = random.randint(0, max_screen_distance) # Random distance between screen and slits (m) + slit_spacing_mm = random.randint(0, max_slit_spacing_mm) # Random slit spacing (mm) + + fringe_spacing = round((((wavelength_nm * 10**-9) * screen_distance) / (slit_spacing_mm * 10**-3)),5) + + problem = f"A laser with a wavelength of ${wavelength_nm}nm$ is shone through a double slit system to produce an interference pattern on a screen. The screen is ${screen_distance}m$ from the slits and the slits are ${slit_spacing_mm}mm$ apart. Calculate the spacing between the bright fringes." + solution = f"Using the equation $\\frac{{\\lambda D}}{{s}}$, we get a fringe spacing of ${fringe_spacing}m$" + return problem, solution + + +