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Chapter 8.6. The math Module

Table of Contents:

Introduction to math module

source: https://docs.python.org/3/library/math.html

The math module provides access to the mathematical functions defined by the C standard. The module offers various functions such as ceiling, floor values, permutations combinations, factorials, GCD (HCF), LCM, etc.

Approximation functions in math module

The math module provides floor, ceil, and trunc functions to perform various mathematical approximations.

round function

Rounding is the process of replacing a precise number by another number of approximately the same value but having fewer digits. example 9.99 can be approximated to 10 by rounding the decimal digits.

The round function does not require math module however other functions related to rounding is available in the module so this function is included in this module.

To perform rounding, we can just call round() method and pass the floating point number to get the rounded integer value.

The round() function takes 1 required argument and 1 optional argument as follows:

  1. number: the number that needs to be rounded
  2. ndigits: the number of decimal digits after which the number is rounded. passing ndigits will return the floating point value instead of int.
x = round(5.85) # 6 (rounded up)

y = round(5.35) # 5 (rounded down)

z = round(4.56678, 3)    # 4.567 (rounded up in the third decimal)

floor function

The floor() function returns the largest integer that is less than or equal to the provided number. The floor() function takes only one argument and returns the integer value.

import math

x = math.floor(5.56) # 5
x = math.floor(-5.56) # -6
y = math.floor(5.0)  # 5

ceil function

The ceil() function returns the smallest integer that is just larger than or equal to the provided number. The ceil() function takes only one argument and returns the integer value.

import math

x = math.ceil(5.56) # 6
x = math.ceil(-5.56) # -5
y = math.ceil(5.0)  # 5

trunc function

The trunc() function drops the fractional part of the floating point number. If the number is negative, it performs ceil() function and if the number is positive, it performs floor() function.

import math

x = math.trunc(5.678)   # 5
x = math.trunc(-5.678)  # -5

Trigonometry

source: https://docs.python.org/3/library/math.html#trigonometric-functions

The math module provides different functions to perform trigonometric measurements. the math function takes angles in radians but not in degrees.

The conversion of radians can be calculated using the formula:

  • $1\pi radians = 180\degree$
  • $1/2\pi^c = 90\degree$

Some of the trigonometric functions that are available in python math module are as follows:

  • math.sin(), math.cos(), math.tan()
  • math.asin(), math.acos(), math.atan()
# 0.5pi = 90 degrees
math.sin(0.5*math.pi)   # 1.0
math.cos(0.5*math.pi)   # 6.123233995736766e-17 ≈ 0.00000000000000006123

# finding out the inverse (arc) of a number
math.asin(0.5)  # 0.5235987755982988 ≈ 30°

The math.dist() function

The math.dist() function finds out the eucledian distance between 2 points. the distance between 2 points is found out using the formula:

  • $distance =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 }$
a = (0, 0)
b = (3, 4)
print(math.dist(a, b))  # 5.0

Angular Conversion

The python math module also offers the conversion between degrees and radians.

print(math.radians(180))      #  3.141592653589793
print(math.degrees(math.pi))  #  180.0

Powers and Exponents

The python math module also provides powerful methods to find different exponential and logarithmic functions.

some of the methods are as follows:

  • math.crbt(x): Returns the cube root of x.
  • math.sqrt(x): Returns the square root of x.
  • math.pow(x, y): Returns the value of $x^y$.
  • math.exp(x): Returns $e^x$ where $e=2.178281..$
  • math.expm1(x): Returns inverse of x.
  • etc.

Example:

print(math.sqrt(16))  # 4.0
print(math.exp(5))    # 148.4131591025766