Python Math

The standard math module covers floats: trig, log, exp, gamma, gcd, hypot, isclose. statistics provides mean/median/stdev; random generates pseudo-random numbers; cmath handles complex numbers.

Python's numeric tower spans integers (unlimited precision), floats (IEEE binary), decimals, and fractions. The math module is for float trigonometry and special functions; statistics summarises data; random samples distributions; cmath extends to complex numbers.

Floating-point equality is approximate: use math.isclose() with suitable tolerances. For money or legal rounding, consider decimal.Decimal instead of binary floats.

Angles in math use radians; convert degrees with math.radians before calling trig functions to avoid silent wrong answers in geometry code.

math: sqrt, log, sin, hypot, isclose, gcd.

statistics: mean, median, mode, variance, stdev (population vs sample).

random: random(), randint, choice, shuffle, seeds and secrets for security.

Complex numbers: 1+2j, cmath, and built-in abs / phase patterns.

NumPy for vectorised arrays (optional, when scale demands it).

Infinity, NaN, and math.isfinite for edge-case checks.

The ** operator and pow() handle integer exponentiation efficiently; math.pow always returns a float. For modular exponentiation in cryptography, use pow(base, exp, mod).

Random numbers from random are pseudo-random and not suitable for passwords or tokens—use the secrets module. Reproducible simulations need an explicit random.seed() or a dedicated random.Random instance.

When datasets grow large, pure-Python loops over math functions become bottlenecks; NumPy or Numba may be warranted, but profile first.

Comparing floats with == without tolerance.

Using random for security-sensitive tokens or session IDs.

Confusing population and sample standard deviation in statistics.stdev vs pstdev.

Integer division confusion: / vs // vs %.

Overflow silently becoming float for very large ints only when mixed with floats in expressions.

Use math.isclose or decimal arithmetic for financial and scientific comparisons.

Pick statistics functions that match your data (sample vs population).

Seed random generators explicitly in notebooks and tests for reproducibility.

Profile before replacing stdlib math with NumPy in hot loops.

Re-read the examples below with these ideas in mind; change variable names and inputs to match your own project.

# Example: math basics
# Run in the REPL or save as a .py file and execute with python.
import math
print(math.pi, math.e)
print(math.sqrt(2), math.log(math.e))

# Example: isclose
# Run in the REPL or save as a .py file and execute with python.
import math
print(0.1 + 0.2 == 0.3)             # False!
print(math.isclose(0.1 + 0.2, 0.3))   # True

# Example: statistics
# Run in the REPL or save as a .py file and execute with python.
import statistics as st
v = [2, 4, 4, 4, 5, 5, 7, 9]
print(st.mean(v), st.median(v), round(st.stdev(v), 2))

# math module wraps C floating-point math functions
import math  # standard math functions
print(math.pi, math.tau)  # circle constants
print(math.sqrt(2), math.hypot(3, 4))  # root and hypotenuse
angle = math.radians(45)  # degrees -> radians
print(math.sin(angle), math.cos(angle))  # trig
print(math.log(100, 10))  # base-10 logarithm -> 2.0
print(math.factorial(6))  # 720
print(math.gcd(48, 18))  # greatest common divisor
print(math.isclose(0.1 + 0.2, 0.3))  # tolerant float compare

# statistics module targets simple descriptive stats
import statistics as stats  # mean/median/stdev helpers
samples = [2.5, 3.1, 2.9, 3.0, 2.8]  # measurements
print(stats.mean(samples))  # arithmetic mean
print(stats.median(samples))  # middle value
print(stats.pstdev(samples))  # population stdev
print(stats.quantiles(samples, n=4))  # quartile cut points
import random  # pseudo-random numbers
random.seed(0)  # reproducible sequence
print(random.random(), random.randint(1, 6))  # float and int