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The math Module in Python: trig, roots, and constants

Beyond + and *, real geometry needs sine, cosine, roots, and pi. The math module supplies them — enough to arrange things on a circle or measure a distance.

The big idea

math provides mathematical constants and functions — math.pi, math.sin, math.cos, math.sqrt — for calculations basic operators can't do.

See it in code

1The basics

The math module supplies constants and functions plain operators can't. math.pi is the circle constant; math.sqrt takes a square root:

python
import math

print("pi is about", math.pi)
print("sqrt(144) is", math.sqrt(144))
Run it — two tools straight from the module:
pi is about 3.141592653589793
sqrt(144) is 12.0

import math unlocks math.pi, math.sqrt, and the trig functions — the tools real geometry needs.

2A step further

The real power is sin and cos, which turn an angle into a point on a circle. This walks four evenly spaced angles and prints each (x, y) — the exact loop we're about to draw with:

python
import math

cx, cy = 250, 250
for i in range(4):
    angle = i * (2 * math.pi / 4)
    x = cx + 160 * math.cos(angle)
    y = cy + 160 * math.sin(angle)
    print(round(x), round(y))
Run it — four angles become four points on a circle:
410 250
250 410
90 250
250 90

Each angle became an (x, y) on a circle of radius 160 centered at (250, 250). Feed those to star instead of print and you've drawn the ring.

3In our world

Now draw it. Same formula, but range(12) for a fuller ring, and instead of printing we hand each (x, y) to star. cos gives the horizontal offset, sin the vertical:

python
import math
from art import Canvas, star

screen = Canvas.create()
Canvas.fill(screen)

cx, cy = 250, 250
for i in range(12):
    angle = i * (2 * math.pi / 12)
    x = cx + 160 * math.cos(angle)
    y = cy + 160 * math.sin(angle)
    star(screen, x, y, size=34)
Run it — twelve stars evenly spaced around a circle:
Twelve stars arranged evenly around the edge of a circle on a dark canvas, like numbers on a clock.

cos(angle) and sin(angle) return values between -1 and 1; multiplying by the radius 160 and adding the center places each star on the ring. The same sine and cosine drive orbits, pendulums, and wave animations.

The same idea, everywhere

math is the backbone of anything geometric or scientific: math.sqrt and the Pythagorean theorem for the distance between two entities, math.hypot as a shortcut, math.floor/math.ceil to snap to a grid, math.log for scales. It works in radians, so remember math.radians() to convert from degrees.

Try it yourself

Compute the distance between two points with math.sqrt((x2 - x1)**2 + (y2 - y1)**2). Then change range(12) to range(24) for a denser ring, and shrink the radius to nest a second circle inside.

The common mistake

Feeding degrees to sin/cos, which expect radians. math.sin(90) is not 1 — it treats 90 as radians. Convert first with math.radians(90), or work in radians from the start as the circle example does.

What it unlocks

The math module builds on imports and operators, and powers curved motion in frames and motion.

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