数学

介绍

Math includes both built-in Python functions and the full math module, which is automatically available in VEXcode IQ (2nd gen). These tools allow you to perform everything from basic arithmetic to advanced trigonometry, rounding, and logarithmic operations.

使用这些函数和常量来计算机器人的位置、角度、距离和其他数值。您还可以在角度和弧度之间转换、计算表达式的值，以及处理无穷大和 NaN 等特殊值。

以下是可用的数学函数、常量和实用程序的列表：

内置函数——Python 附带的常见数学工具。

• 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.

三角学——计算角度和边之间的关系。

• 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.

舍入和绝对值——调整精度或方向。

• 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.

指数和对数——幂、根和对数计算。

• math.pow – Raises a number to a power.

• math.sqrt – Returns the square root.

• math.exp – Calculates e to the power of x.

• math.log – Natural logarithm (base e).

浮点运算——检查或分解浮点值。

• 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).

内置函数

Python 提供了几个内置函数，允许您在项目内部执行数学运算。

abs

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

Usage:
abs(x)

范围	描述
x	整数或浮点数。

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

# abs_result = 10

round

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

Usage:
round(x, ndigits)

范围	描述
x	整数或浮点数。
ndigits	可选。要四舍五入的小数位数。默认值为 0。

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

# round_int_result = 6

# Round 3.14159 to 2 decimal places
round_result = round(3.14159, 2)
brain.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)

范围	描述
arg1, arg2, …	要比较的数字。
sequence	包含数字的列表、元组或其他序列。

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

# min_result = 1

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

范围	描述
arg1, arg2, …	要比较的数字。
sequence	包含数字的列表、元组或其他序列。

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

# max_result = 7

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

范围	描述
sequence	包含数字的列表、元组或其他序列。
start	可选。要添加到总和的值。默认值为 0。

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

范围	描述
a	股息。
b	除数。

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

范围	描述
x	基数。
y	指数。
mod	Optional. A modulus value. If provided, returns (x ** y) % mod.

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

# pow_result = 8

int

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

Usage:
int(x, base)

范围	描述
x	要转换的数字、字符串或其他对象。
base	可选。用于转换的进制数。默认值为 10。

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

# Output: 19 coins

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

# Output: 110

float

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

Usage:
float(x)

范围	描述
x	要转换的数字、字符串或其他对象。

# Convert division result to a float
num_apples = 6
num_people = 2
apples_per_person = float(num_apples) / num_people
brain.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)
brain.screen.print(user_number * 3)

# Output: 70.20

数学模块

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

常量是预定义的值，在项目执行过程中保持不变。它们可以在计算中使用，无需任何定义或赋值。

圆周率

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
brain.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
brain.screen.print(circumference)

# circumference = 31.42

e

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)
brain.screen.print(e_power)

# e_power = 7.39

Trigonometry

罪

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

Usage:
math.sin(x)

范围	描述
x	表示弧度角的浮点数或整数。

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

# result = 0.50

余弦

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

Usage:
math.cos(x)

范围	描述
x	表示弧度角的浮点数或整数。

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

# result = 0.50

棕褐色

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

Usage:
math.tan(x)

范围	描述
x	表示弧度角的浮点数或整数。

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

# result = 1.00

阿坦

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

Usage:
math.atan(x)

范围	描述
x	浮点数或整数。

# Calculate the arc tangent 
# of 1 in degrees
arc_tan = math.atan(1.0)
result = math.degrees(arc_tan)
brain.screen.print(result)

# result = 45.00

反义词

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)

范围	描述
y	表示 y 坐标的浮点数或整数。
x	表示 x 坐标的浮点数或整数。

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

# result = 45.00

阿辛

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

Usage:
math.asin(x)

范围	描述
x	-1 到 1 之间的浮点数或整数。

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

# result = 30.00

阿科斯

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

Usage:
math.acos(x)

范围	描述
x	-1 到 1 之间的浮点数或整数。

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

# result = 60.00

度

degrees converts an angle from radians to degrees.

Usage:
math.degrees(x)

范围	描述
x	表示弧度角的浮点数或整数。

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

# degrees_result = 180.00

弧度

radians converts an angle from degrees to radians.

Usage:
math.radians(x)

范围	描述
x	表示角度（以度为单位）的浮点数或整数。

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

# radians_result = 3.14

Rounding & Absolute Values

天花板

ceil rounds a number up to the nearest integer.

Usage:
math.ceil(x)

范围	描述
x	要向上舍入的浮点数或整数。

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

# ceil_result = 4

地面

floor rounds a number down to the nearest integer.

Usage:
math.floor(x)

范围	描述
x	要向下舍入的浮点数或整数。

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

# floor_result = 3

截断

trunc removes the decimal part of a number without rounding.

Usage:
math.trunc(x)

范围	描述
x	要截断的浮点数。

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

# trunc_result = 3

晶圆厂

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

Usage:
math.fabs(x)

范围	描述
x	浮点数或整数。

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

# fabs_result = 3.70

Exponents & Logarithms

战俘

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

Usage:
math.pow(x, y)

范围	描述
x	浮点数或整数基数。
y	浮点数或整数指数。

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

# power_result = 8.00

平方根

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

Usage:
math.sqrt(x)

范围	描述
x	非负浮点数或整数。

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

# sqrt_result = 4.00

经验值

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

Usage:
math.exp(x)

范围	描述
x	浮点数或整数。

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

# exp_result = 2.72

日志

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

Usage:
math.log(x)

范围	描述
x	正浮点数或整数。

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

# log_result = 2.00

Floating Point Operations

修改

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)

范围	描述
x	要分解的浮点数或整数。

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

范围	描述
x	要分解的浮点数或整数。

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

# mantissa = 0.50
# exponent = 5

fmod

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

Usage:
math.fmod(x, y)

范围	描述
x	股息。
y	除数。

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

# fmod_result = 1.00

版权声明

copysign returns x with the sign of y.

Usage:
math.copysign(x, y)

范围	描述
x	要修改的值。
y	其符号将被复制的值。

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

范围	描述
x	基值。
exp	指数。

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

# ldexp_result = 48.00