from turtle import (
    right,
    color,
    goto,
    pensize
)
from math import sin, cos, tau, pi

def cardioid(theta, size=100):
    return size * (1 - sin(theta))

def polar_to_cartesian(coord: tuple[float, float]):
    r, theta = coord
    return (r * cos(theta), r * sin(theta))

def get_segmented_cardioid(segments = 16):
    angles = [pi / 2 + i * (tau/ segments) for i in range(segments + 1)]
    radii = map(cardioid, angles)
    return list(map(polar_to_cartesian, zip(radii, angles)))  

segments = 50
coords = get_segmented_cardioid(segments)
color(1, 0, 0)
pensize(5)
for i in range(segments + 1):
    goto(coords[i])
right(90)
input()