Matemáticas#

Introducción#

Math includes both built-in Python functions and the full math module, which is automatically available in VEXcode AIM. These tools allow you to perform everything from basic arithmetic to advanced trigonometry, rounding, and logarithmic operations.

Usa estas funciones y constantes para calcular posiciones, ángulos, distancias y otros valores numéricos para tu robot. También puedes convertir entre grados y radianes, evaluar expresiones y trabajar con valores especiales como infinito y NaN.

A continuación se muestra una lista de funciones matemáticas, constantes y utilidades disponibles:

Funciones integradas: herramientas matemáticas comunes incluidas con Python.

  • abs – Returns the absolute value of a number.

  • round – Rounds a number to a specified number of decimal places.

  • min – Returns the smallest of the input values.

  • max – Returns the largest of the input values.

  • sum – Adds up all values in an iterable.

  • divmod – Returns the quotient and remainder as a tuple.

  • pow – Raises a number to a power, optionally with a modulus.

  • int – Converts a value to an integer.

  • float – Converts a value to a floating-point number.

Constants – Predefined values from the math module.

  • math.pi – The constant π (pi).

  • math.tau – The constant tau (2π).

  • math.e – Euler’s number, base of the natural log.

  • math.inf – Positive infinity.

  • math.nan – Not a Number (NaN).

Trigonometría – Calcular ángulos y relaciones entre lados.

  • math.sin – Sine of an angle in radians.

  • math.cos – Cosine of an angle in radians.

  • math.tan – Tangent of an angle in radians.

  • math.atan – Arctangent of a value in radians.

  • math.atan2 – Arctangent of y/x in radians, considering the quadrant.

  • math.asin – Arcsine of a value in radians.

  • math.acos – Arccosine of a value in radians.

  • math.degrees – Converts radians to degrees.

  • math.radians – Converts degrees to radians.

Hiperbólicas: funciones trigonométricas avanzadas.

Redondeo y valor absoluto: ajuste la precisión o la dirección.

  • math.ceil – Rounds up to the nearest integer.

  • math.floor – Rounds down to the nearest integer.

  • math.trunc – Removes the decimal portion.

  • math.fabs – Returns the absolute value as a float.

Exponentes y logaritmos: cálculos de potencia, raíz y logaritmo.

Operaciones de punto flotante: inspeccionar o descomponer valores flotantes.

  • math.modf – Returns the fractional and integer parts of a float.

  • math.frexp – Decomposes a number into mantissa and exponent.

  • math.fmod – Remainder with sign of the dividend.

  • math.copysign – Returns a value with the sign of another.

  • math.ldexp – Computes x * (2 ** exp).

Comparación y aproximación: verifique valores con tolerancias o categorías.

Error y Gamma – Funciones matemáticas especiales.

Funciones integradas#

Python proporciona varias funciones integradas que le permiten realizar operaciones matemáticas dentro de su proyecto.

abs#

abs returns the absolute value of a number, removing any negative sign.

Usage:
abs(x)

Parámetro

Descripción

x

Un número entero o flotante.

 
# Get the absolute value of -10
abs_result = abs(-10)
robot.screen.print(abs_result)

# abs_result = 10

round#

round rounds a number to a specified number of decimal places.

Usage:
round(x, ndigits)

Parámetro

Descripción

x

Un número entero o flotante.

ndigits

Opcional. El número de decimales a redondear. El valor predeterminado es 0.

 
# Round 5.7 to the nearest integer
round_int_result = round(5.7)
robot.screen.print(round_int_result)

# round_int_result = 6


# Round 3.14159 to 2 decimal places
round_result = round(3.14159, 2)
robot.screen.print(round_result)

# round_result = 3.14

min#

min returns the smallest value from multiple arguments or an iterable.

Usage:
min(arg1, arg2, …) or min(sequence)

Parámetro

Descripción

arg1, arg2, …

Los números para comparar.

sequence

Una lista, tupla u otra secuencia que contiene números.

 
# Get the smallest number from 3, 7, and 1
min_result = min(3, 7, 1)
robot.screen.print(min_result)

# min_result = 1


# Get the smallest value from a list
min_list_result = min([10, 4, 25, 1])
robot.screen.print(min_list_result)

# min_list_result = 1

max#

max returns the largest value from multiple arguments or an iterable.

Usage:
max(arg1, arg2, …) or max(sequence)

Parámetro

Descripción

arg1, arg2, …

Los números para comparar.

sequence

Una lista, tupla u otra secuencia que contiene números.

 
# Get the largest number from 3, 7, and 1
max_result = max(3, 7, 1)
robot.screen.print(max_result)

# max_result = 7


# Get the largest value from a list
max_list_result = max([10, 4, 25, 1])
robot.screen.print(max_list_result)

# max_list_result = 25

sum#

sum adds up all values in an iterable, with an optional starting value.

Usage:
sum(sequence, start)

Parámetro

Descripción

sequence

Una lista, tupla u otra secuencia que contiene números.

start

Opcional. Un valor para añadir a la suma. El valor predeterminado es 0.

 
# Calculate the sum of a list of numbers
sum_result = sum([1, 2, 3, 4, 5])
robot.screen.print(sum_result)

# sum_result = 15


# Calculate the sum of a list with a starting value of 10
sum_with_start = sum([1, 2, 3], 10)
robot.screen.print(sum_with_start)

# sum_with_start = 16

divmod#

divmod returns a tuple containing the quotient and remainder of a division operation.

Usage:
divmod(a, b)

Parámetro

Descripción

a

El dividendo.

b

El divisor.

 
# Perform integer division and remainder of 10 / 3
divmod_result = divmod(10, 3)
robot.screen.print(divmod_result)

# divmod_result = (3, 1)

pow#

pow raises a number to a power and optionally performs a modulus operation.

Usage:
pow(x, y, mod)

Parámetro

Descripción

x

El número base.

y

El exponente.

mod

Optional. A modulus value. If provided, returns (x ** y) % mod.

 
# Calculate 2 raised to the power of 3
pow_result = pow(2, 3)
robot.screen.print(pow_result)

# pow_result = 8


# Calculate (5 ** 3) % 7
pow_mod_result = pow(5, 3, 7)
robot.screen.print(pow_mod_result)

# pow_mod_result = 6

int#

int converts a number or string into an integer. It also supports base conversion when converting from a string.

Usage:
int(x, base)

Parámetro

Descripción

x

Un número, cadena u otro objeto para convertir.

base

Opcional. La base numérica que se usará para la conversión. El valor predeterminado es 10.

 
# Convert a float to an integer to get rid of decimals
price = 19.99
price_int = int(price)
robot.screen.print(f"{price_int} coins")

# Output: 19 coins


# Convert a string into an integer to use in calculations
user_input = "55"
user_number = int(user_input)
robot.screen.print(user_number * 2)

# Output: 110

float#

float converts a number or string into a floating-point number.

Usage:
float(x)

Parámetro

Descripción

x

Un número, cadena u otro objeto para convertir.

 
# Convert division result to a float
num_apples = 6
num_people = 2
apples_per_person = float(num_apples) / num_people
robot.screen.print(apples_per_person)

# Output: 3.00


# Convert a string into a float to use in calculations
user_input = "23.4"
user_number = float(user_input)
robot.screen.print(user_number * 3)

# Output: 70.20

Módulo de Matemáticas#

The math module in MicroPython provides additional methods for performing common mathematical calculations. These methods include trigonometric, logarithmic, and other numerical operations.

The math module is imported by default in VEXcode.

Constants#

Las constantes son valores predefinidos que permanecen fijos durante un proyecto. Pueden utilizarse en cálculos sin necesidad de definirlas ni asignarlas.

pi#

pi gives the mathematical constant π, the ratio of a circle’s circumference to its diameter.

Usage:
math.pi

# Calculate the area of a circle with radius 5 using pi
circle_area = math.pi * 5 * 5
robot.screen.print(circle_area)

# circle_area = 78.54

tau#

tau gives the value of 2π.

Usage:
math.tau

# Calculate the circumference of a circle with radius
circumference = math.tau * 5
robot.screen.print(circumference)

# circumference = 31.42

mi#

e gives the base of the natural logarithm.

Usage:
math.e

# Calculate e raised to the power of 2
e_power = math.pow(math.e, 2)
robot.screen.print(e_power)

# e_power = 7.39

información#

inf gives positive infinity as a float.

Usage:
math.inf

# Check if infinity is infinite
inf_value = math.inf

if math.isinf(inf_value):
    robot.screen.print("Infinity")

# Prints "Infinity"

yaya#

nan represents a special float for “Not a Number” (NaN).

Usage:
math.nan

# Check if nan is Not a Number
nan_value = math.nan

if math.isnan(nan_value):
    robot.screen.print("Not a Number")

# Prints "Not a Number"

Trigonometry#

pecado#

sin calculates the sine of an angle in radians and returns a float.

Usage:
math.sin(x)

Parámetro

Descripción

x

Un flotante o entero que representa un ángulo en radianes.

 
# Calculate the sine of 30 degrees in radians
sine_result = math.sin(math.radians(30))
robot.screen.print(sine_result)

# sine_result = 0.50

porque#

cos calculates the cosine of an angle in radians and returns a float.

Usage:
math.cos(x)

Parámetro

Descripción

x

Un flotante o entero que representa un ángulo en radianes.

 
# Calculate the cosine of 60 degrees in radians
cosine_result = math.cos(math.radians(60))
robot.screen.print(cosine_result)

# cosine_result = 0.50

broncearse#

tan calculates the tangent of an angle in radians and returns a float.

Usage:
math.tan(x)

Parámetro

Descripción

x

Un flotante o entero que representa un ángulo en radianes.

 
# Calculate the tangent of 45 degrees in radians
tangent_result = math.tan(math.radians(45))
robot.screen.print(tangent_result)

# tangent_result = 1.00

Atán#

atan calculates the inverse tangent (arc tangent) of a number and returns a float representing the angle in radians.

Usage:
math.atan(x)

Parámetro

Descripción

x

Un flotante o entero.

 
# Calculate the arc tangent of 1 in degrees
arc_tangent_result = math.degrees(math.atan(1.0))
robot.screen.print(arc_tangent_result)

# arc_tangent_result = 45.00

atan2#

atan2 calculates the principal value of the inverse tangent of y/x and returns a float representing the angle in radians.

Usage:
math.atan2(y, x)

Parámetro

Descripción

y

Un número flotante o entero que representa la coordenada y.

x

Un número flotante o entero que representa la coordenada x.

 
# Calculate the inverse tangent of 1/1 in degrees
atan2_result = math.degrees(math.atan2(1.0, 1.0))
robot.screen.print(atan2_result)

# atan2_result = 45.00

asiático#

asin calculates the inverse sine (arc sine) of a number and returns a float representing the angle in radians.

Usage:
math.asin(x)

Parámetro

Descripción

x

Un número flotante o entero entre -1 y 1.

 
# Calculate the arc sine of 0.5 in degrees
arc_sine_result = math.degrees(math.asin(0.5))
robot.screen.print(arc_sine_result)

# arc_sine_result = 30.00

acos#

acos calculates the inverse cosine (arc cosine) of a number and returns a float representing the angle in radians.

Usage:
math.acos(x)

Parámetro

Descripción

x

Un número flotante o entero entre -1 y 1.

 
# Calculate the arc cosine of 0.5 in degrees
arc_cosine_result = math.degrees(math.acos(0.5))
robot.screen.print(arc_cosine_result)

# arc_cosine_result = 60.00

grados#

degrees converts an angle from radians to degrees.

Usage:
math.degrees(x)

Parámetro

Descripción

x

Un flotante o entero que representa un ángulo en radianes.

 
# Convert pi radians to degrees
degrees_result = math.degrees(math.pi)
robot.screen.print(degrees_result)

# degrees_result = 180.00

radianes#

radians converts an angle from degrees to radians.

Usage:
math.radians(x)

Parámetro

Descripción

x

Un número flotante o entero que representa un ángulo en grados.

 
# Convert 180 degrees to radians
radians_result = math.radians(180)
robot.screen.print(radians_result)

# radians_result = 3.14

Hyperbolics#

Sinh#

sinh calculates the hyperbolic sine of x.

Usage:
math.sinh(x)

Parámetro

Descripción

x

Un flotante o entero que representa el valor de entrada.

 
# Calculate the hyperbolic sine of 1
sinh_result = math.sinh(1)
robot.screen.print(sinh_result)

# sinh_result = 1.18

aporrear#

cosh calculates the hyperbolic cosine of x.

Usage:
math.cosh(x)

Parámetro

Descripción

x

Un flotante o entero que representa el valor de entrada.

 
# Calculate the hyperbolic cosine of 1
cosh_result = math.cosh(1)
robot.screen.print(cosh_result)

# cosh_result = 1.54

tanh#

tanh calculates the hyperbolic tangent of x.

Usage:
math.tanh(x)

Parámetro

Descripción

x

Un flotante o entero que representa el valor de entrada.

 
# Calculate the hyperbolic tangent of 1
tanh_result = math.tanh(1)
robot.screen.print(tanh_result)

# tanh_result = 0.76

asiático#

asinh calculates the inverse hyperbolic sine of x.

Usage:
math.asinh(x)

Parámetro

Descripción

x

Un flotante o entero que representa el valor de entrada.

 
# Calculate the inverse hyperbolic sine of 1
asinh_result = math.asinh(1)
robot.screen.print(asinh_result)

# asinh_result = 0.88

acosh#

acosh calculates the inverse hyperbolic cosine of x.

Usage:
math.acosh(x)

Parámetro

Descripción

x

Un flotante o entero mayor o igual a 1.

 
# Calculate the inverse hyperbolic cosine of 2
acosh_result = math.acosh(2)
robot.screen.print(acosh_result)

# acosh_result = 1.32

Atanh#

atanh calculates the inverse hyperbolic tangent of x.

Usage:
math.atanh(x)

Parámetro

Descripción

x

Un flotante entre -1 y 1 (exclusivo).

 
# Calculate the inverse hyperbolic tangent of 0.5
atanh_result = math.atanh(0.5)
robot.screen.print(atanh_result)

# atanh_result = 0.55

Rounding & Absolute Values#

fortificar techo#

ceil rounds a number up to the nearest integer.

Usage:
math.ceil(x)

Parámetro

Descripción

x

Un número flotante o entero que se redondeará hacia arriba.

 
# Round 3.7 up to the nearest integer
ceil_result = math.ceil(3.7)
robot.screen.print(ceil_result)

# ceil_result = 4

piso#

floor rounds a number down to the nearest integer.

Usage:
math.floor(x)

Parámetro

Descripción

x

Un número flotante o entero que se redondeará hacia abajo.

 
# Round 3.7 down to the nearest integer
floor_result = math.floor(3.7)
robot.screen.print(floor_result)

# floor_result = 3

tronco#

trunc removes the decimal part of a number without rounding.

Usage:
math.trunc(x)

Parámetro

Descripción

x

Un flotador que debe truncarse.

 
# Remove the decimal part of 3.7
trunc_result = math.trunc(3.7)
robot.screen.print(trunc_result)

# trunc_result = 3

fábricas#

fabs returns the absolute value of a number as a float.

Usage:
math.fabs(x)

Parámetro

Descripción

x

Un flotante o entero.

 
# Get the absolute value of -3.7
fabs_result = math.fabs(-3.7)
robot.screen.print(fabs_result)

# fabs_result = 3.70

Exponents & Logarithms#

poder#

pow raises x to the power of y and returns a float, even if both inputs are integers.

Usage:
math.pow(x, y)

Parámetro

Descripción

x

Una base de número flotante o entero.

y

Un exponente flotante o entero.

 
# Calculate 2 raised to the power of 3
power_result = math.pow(2, 3)
robot.screen.print(power_result)

# power_result = 8.00

raíz cuadrada#

sqrt calculates the square root of a number and returns a float, even for perfect squares.

Usage:
math.sqrt(x)

Parámetro

Descripción

x

Un número entero o flotante no negativo.

 
# Calculate the square root of 16
sqrt_result = math.sqrt(16)
robot.screen.print(sqrt_result)

# sqrt_result = 4.00

exp#

exp calculates the exponential of a number and returns a float.

Usage:
math.exp(x)

Parámetro

Descripción

x

Un flotante o entero.

 
# Calculate e raised to the power of 1
exp_result = math.exp(1)
robot.screen.print(exp_result)

# exp_result = 2.72

registro#

log calculates the natural logarithm of a number and returns a float.

Usage:
math.log(x)

Parámetro

Descripción

x

Un número entero o flotante positivo.

 
# Calculate the natural logarithm (base e) of 7.389056
log_result = math.log(7.389056)
robot.screen.print(log_result)

# log_result = 2.00

registro10#

log10 calculates the base-10 logarithm of a number and returns a float.

Usage:
math.log10(x)

Parámetro

Descripción

x

Un número entero o flotante positivo.

 
# Calculate the base-10 logarithm of 1000
log10_result = math.log10(1000)
robot.screen.print(log10_result)

# log10_result = 3.00

registro2#

log2 calculates the base-2 logarithm of a number and returns a float, even when x is a power of 2.

Usage:
math.log2(x)

Parámetro

Descripción

x

Un número entero o flotante positivo.

 
# Calculate the base-2 logarithm of 8
log2_result = math.log2(8)
robot.screen.print(log2_result)

# log2_result = 3.00

factorial#

factorial returns the factorial of an integer x, which is the product of all positive integers up to x.

Usage:
math.factorial(x)

Parámetro

Descripción

x

Un número entero no negativo.

 
# Calculate 5 factorial (5!)
factorial_result = math.factorial(5)
robot.screen.print(factorial_result)

# factorial_result = 120

expm1#

expm1 calculates ex - 1, which is more accurate for small x.

Usage:
math.expm1(x)

Parámetro

Descripción

x

El valor del exponente.

 
# Compute expm1(1) (e^1 - 1)
expm1_result = math.expm1(1)
robot.screen.print(expm1_result)

# expm1_result = 1.72

Floating Point Operations#

modf#

modf decomposes a number into its fractional and integer parts and returns a tuple (fractional part, integer part), both as floats.

Usage:
math.modf(x)

Parámetro

Descripción

x

Un flotante o entero para descomponer.

 
# Decompose 3.14159 into fractional and integer parts
fractional_part, integer_part = math.modf(3.14159)
robot.screen.print(fractional_part)
robot.screen.next_row()
robot.screen.print(integer_part)

# fractional_part = 0.14
# integer_part = 3.00

frexp#

frexp decomposes a number into its mantissa and exponent and returns a tuple (mantissa, exponent), where the mantissa is a float and the exponent is an integer.

Usage:
math.frexp(x)

Parámetro

Descripción

x

Un flotante o entero para descomponer.

 
# Decompose 16 into its mantissa and exponent
mantissa, exponent = math.frexp(16)
robot.screen.print(mantissa)
robot.screen.next_row()
robot.screen.print(exponent)

# mantissa = 0.50
# exponent = 5

modo de funcionamiento#

fmod returns the remainder of division while keeping the sign of the dividend (x).

Usage:
math.fmod(x, y)

Parámetro

Descripción

x

El dividendo.

y

El divisor.

 
# Calculate remainder of 10 / 3
# that preserves the sign of 10
fmod_result = math.fmod(10, 3)
robot.screen.print(fmod_result)

# fmod_result = 1.00

firma de derechos de autor#

copysign returns x with the sign of y.

Usage:
math.copysign(x, y)

Parámetro

Descripción

x

El valor a modificar.

y

El valor cuyo signo se copiará.

 
# Return -10 with the sign of 3 (positive)
copysign_result = math.copysign(-10, 3)
robot.screen.print(copysign_result)

# copysign_result = 10.00

ldexp#

ldexp computes x * (2 ** exp), which is equivalent to x * 2exp{code}.

Usage:
math.ldexp(x, exp)

Parámetro

Descripción

x

El valor base.

exp

El exponente.

 
# Compute 3 * (2 ** 4)
ldexp_result = math.ldexp(3, 4)
robot.screen.print(ldexp_result)

# ldexp_result = 48.00

Comparison & Approximation#

está cerca#

isclose checks if two numbers are approximately equal within a tolerance.

Usage:
math.isclose(a, b, rel_tol, abs_tol)

Parámetro

Descripción

a

El primer número a comparar.

b

El segundo número a comparar.

rel_tol

Opcional. La diferencia máxima permitida entre a y b, en relación con su tamaño. El valor predeterminado es 1e-09 (muy pequeño).

abs_tol

Opcional. Un margen de error fijo, útil al comparar números cercanos a cero. El valor predeterminado es 0.0.

Note: If both rel_tol and abs_tol are provided, whichever condition is met first determines the result.

# Check if 1.000000001 and 1.0 are close
# within the default tolerance
isclose_result = math.isclose(1.000000001, 1.0)
robot.screen.print(isclose_result)

# isclose_result = True


# Check if 0.0000001 and 0.0 are close
# using absolute tolerance
isclose_result = math.isclose(0.0000001, 0.0, abs_tol=1e-07)
robot.screen.print(isclose_result)

# isclose_result = True


# Check if 1000000.0 and 1000000.1 are close
# with a stricter tolerance
isclose_result = math.isclose(1000000.0, 1000000.1, rel_tol=1e-10)
robot.screen.print(isclose_result)

# isclose_result = False

es finito#

isfinite checks if a number is finite. This method returns a Boolean value:

  • True - The number is finite.

  • False - The number is infinite.

Usage:
math.isfinite(x)

Parámetro

Descripción

x

Un flotante o entero para comprobar.

 
# Check if 42 is a finite number (returns True)
is_finite_true = math.isfinite(42)
robot.screen.print(is_finite_true)

# is_finite_true = True


# Check if infinity is a finite number (returns False)
is_finite_false = math.isfinite(math.inf)
robot.screen.print(is_finite_false)

# is_finite_false = False

es inf#

isinf checks if a number is infinite. This method returns a Boolean value:

  • True - The number is infinite.

  • False - The number is finite.

Usage:
math.isinf(x)

Parámetro

Descripción

x

Un flotante o entero para comprobar.

 
# Check if infinity is an infinite number (returns True)
is_inf_true = math.isinf(math.inf)
robot.screen.print(is_inf_true)

# is_inf_true = True


# Check if 42 is an infinite number (returns False)
is_inf_false = math.isinf(42)
robot.screen.print(is_inf_false)

# is_inf_false = False

Isnan#

isnan checks if a number is NaN (Not a Number). This method returns a Boolean value:

  • True - The number is NaN.

  • False - The number is a valid number.

Usage:
math.isnan(x)

Parámetro

Descripción

x

Un flotante o entero para comprobar.

 
# Check if NaN (Not a Number) is NaN (returns True)
is_nan_true = math.isnan(math.nan)
robot.screen.print(is_nan_true)

# is_nan_true = True


# Check if 42 is NaN (returns False)
is_nan_false = math.isnan(42)
robot.screen.print(is_nan_false)

# is_nan_false = False

Error and Gamma Calculations#

gama#

gamma computes the gamma function of x, which generalizes the factorial function for real and complex numbers. For an integer n, gamma(n) = (n-1)!.

Usage:
math.gamma(x)

Parámetro

Descripción

x

Un número entero o flotante positivo.

 
# Calculate the gamma function of 5 (equivalent to 4!)
gamma_result = math.gamma(5)
robot.screen.print(gamma_result)

# gamma_result = 24.00

lgamma#

lgamma computes the natural logarithm of the gamma function.

Usage:
math.lgamma(x)

Parámetro

Descripción

x

Un número entero o flotante positivo.

 
# Calculate the natural logarithm of the
# gamma function of 5
lgamma_result = math.lgamma(5)
robot.screen.print(lgamma_result)

# lgamma_result = 3.18

erf#

erf computes the error function of x.

Usage:
math.erf(x)

Parámetro

Descripción

x

Un flotante o entero que representa el valor de entrada.

 
# Calculate the error function of 1
erf_result = math.erf(1)
robot.screen.print(erf_result)

# erf_result = 0.84

erfc#

erfc computes the complementary error function of x, which is defined as 1 - erf(x).

Usage:
math.erfc(x)

Parámetro

Descripción

x

Un flotante o entero que representa el valor de entrada.

 
# Calculate the complementary error function of 1
erfc_result = math.erfc(1)
robot.screen.print(erfc_result)

# erfc_result = 0.16
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