Math Module

Python provides powerful mathematical capabilities through both built-in functions and the math module. From basic operations like finding minimum/maximum values to advanced functions like trigonometry, logarithms, and factorials - Python has you covered for scientific computing, game development, data analysis, and any math-heavy application!

Built-in Math Functions

Python includes several math functions that don't require any imports. These built-in functions handle common operations: finding extremes with min() and max(), absolute values with abs(), powers with pow(), and rounding with round(). They work with both integers and floats.

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The math Module Basics

The math module provides essential mathematical functions: square roots, ceiling/floor operations, and important constants like pi and e. Unlike built-in functions, you must import the math module first.

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Trigonometric Functions

The math module provides all standard trigonometric functions: sine, cosine, tangent, and their inverses. Important: All angles are in radians, not degrees! Use math.radians() to convert degrees to radians, and math.degrees() for the reverse conversion.

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Advanced Math Functions

Beyond basics, the math module offers factorials, combinations/permutations, logarithms, GCD/LCM, and special value checking. These are invaluable for statistics, cryptography, combinatorics, and scientific applications.

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Common Mistakes

import math

# Wrong - 90 is interpreted as radians!
result = math.sin(90)
print(result)  # 0.893... (not 1!)

# Correct - convert to radians first
result = math.sin(math.radians(90))
print(result)  # 1.0

# Wrong - NameError!
result = sqrt(16)

# Correct options:
import math
result = math.sqrt(16)

# Or import specific function
from math import sqrt
result = sqrt(16)

# Python 3: / always returns float
print(5 / 2)   # 2.5

# Use // for integer division
print(5 // 2)  # 2

# math.floor vs //
import math
print(math.floor(-7/2))  # -4 (floor)
print(-7 // 2)           # -4 (same)
print(int(-7/2))         # -3 (truncation!)

import math

# Wrong - floating point errors!
if 0.1 + 0.2 == 0.3:
    print("Equal")  # Never prints!

# Correct - use isclose()
if math.isclose(0.1 + 0.2, 0.3):
    print("Equal")  # Prints!

# Or specify tolerance
if math.isclose(a, b, rel_tol=1e-9, abs_tol=1e-9):
    print("Close enough")

import math

# Wrong - math.sqrt can't handle negative!
result = math.sqrt(-1)  # ValueError!

# For complex numbers, use cmath
import cmath
result = cmath.sqrt(-1)
print(result)  # 1j (imaginary unit)

# Or check first
n = -1
if n >= 0:
    result = math.sqrt(n)
else:
    print("Cannot calculate sqrt of negative")

Exercise: Geometry Calculator

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import math

def circle_area(radius):
    """Calculate area of a circle: pi * r^2"""
    return math.pi * radius ** 2

def hypotenuse(a, b):
    """Calculate hypotenuse using Pythagorean theorem."""
    # Could also use: math.sqrt(a**2 + b**2)
    return math.hypot(a, b)

def distance(x1, y1, x2, y2):
    """Calculate distance between two points."""
    # Could also use: math.sqrt((x2-x1)**2 + (y2-y1)**2)
    return math.dist((x1, y1), (x2, y2))

# Test the functions
print(f"Circle area (r=5): {circle_area(5):.2f}")
print(f"Hypotenuse (3, 4): {hypotenuse(3, 4)}")
print(f"Distance (0,0) to (3,4): {distance(0, 0, 3, 4)}")

Summary

What's Next?

Now that you can handle mathematical operations, let's learn about the json module for working with JSON data - the universal format for data exchange in web APIs, configuration files, and modern applications!