Draw minimal coprime stars

star.py

# see https://stackoverflow.com/questions/72943585/how-to-draw-n-pointed-stars-using-turtle#comment140920249_72943585

import math
from turtle import Screen, Turtle


def first_coprime(n):
    for k in range(2, n):
        if math.gcd(n, k) == 1:
            return k

    return None


n = 10
step = first_coprime(n)
radius = 200

points = []
for i in range(n):
    angle = 2 * math.pi * i / n  # Angle in radians
    x = radius * math.cos(angle)
    y = radius * math.sin(angle)
    points.append((x, y))

t = Turtle()
t.speed(0)
t.penup()
t.goto(points[0])
t.pendown()

i = 0
for _ in range(n):
    t.goto(points[i])
    i = (i + step) % n

t.goto(points[0])
t.hideturtle()
Screen().exitonclick()