Python draw n-pointed star with turtle graphics

Question

My professor has asked our class to write a Python function that does as following:

Draw a regular n-pointed star with side d - in a function named star(turtle, n, d)

Here's the code that I have so far:

def star(turtle, n, d):
    angle = (180-((180*(n-2))/n))*2
    for i in range(n):
        t.forward(d)
        t.left(angle)
    return angle

The problem that I am experiencing is that my function is only able to draw stars with odd numbers of corners (5, 7, 9-sided stars). When I ask it to draw a star with an even number of sides, it outputs polygon with sides n/2. So asking to draw an 8-sided star outputs a square, 6-sided gives a triangle, and so forth.

I've tried altering the angle formula many times, but it never works with any given n.

Thanks for helping!

Answer 1

You can draw most of the odd and even pointed stars with the same code by using a GCD routine to look for coprimes and treating failures as exceptions:

import sys
import turtle
from time import sleep

def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a

def normal_star(size, color, points):
    if points <= 4:
        raise ValueError('Not enough points')

    turtle.color(color)

    for coprime in range(points // 2, 1, -1):
        if gcd(points, coprime) == 1:

            print("({},{})".format(points, coprime), file=sys.stderr)

            start = turtle.position()

            for _ in range(points):
                turtle.forward(size)
                turtle.left(360.0 / points * coprime)

            turtle.setposition(start)

            return

    abnormal_star(size, color, points)

def abnormal_star(size, color, points):
    # deal with special cases here
    print("Exception:", points, file=sys.stderr)

for points in range(5, 20):
    turtle.reset()
    normal_star(200, 'red', points)
    sleep(5)

turtle.exitonclick()

For points from 5 to 20, this only fails to find a solution for 6 which you'll need to treat as an exception, i.e. specialized code or just letting the user know it's an exception you can't handle:

> python3 test.py
(5,2)
Exception: 6
(7,3)
(8,3)
(9,4)
(10,3)
(11,5)
(12,5)
(13,6)
(14,5)
(15,7)
(16,7)
(17,8)
(18,7)
(19,9)
(20,9)
>

Output example for arguments 200,'red',10