Stars of Different Sizes

By the end of this lab you'll be able to:

• Draw a 5-pointed star using the 144° exterior angle trick
• Write a star(x, y, size, color) function with four parameters
• Scatter multiple stars across the canvas using random

Fifteen gold and red stars of various sizes are scattered across a dark canvas, each one drawn with the same five-line trick — a perfect polygon shortcut.

Welcome to Stars of Different Sizes!

Did you know you can draw a 5-pointed star by turning 144° at each point? In this lab you'll learn why, then scatter stars of different sizes across the canvas! Let's code it together!

How the Star Works

A 5-pointed star's exterior angle is 144° (not the usual polygon 360 / 5 = 72°). This is because the star skips over one vertex each time, so the effective angle is 2 × 72° = 144°. Five sides × 144° = 720° = two full rotations — which is exactly how a star point works geometrically.

Sample Code

import turtle
import random
monty = turtle.Turtle()
monty.speed(0)
monty.hideturtle()
monty.screen().bgcolor('black') if hasattr(monty, 'screen') else None
random.seed(7)

def star(x, y, size, color):
    monty.penup()
    monty.goto(x, y)
    monty.pendown()
    monty.color(color)
    monty.begin_fill()
    for _ in range(5):
        monty.forward(size)
        monty.right(144)
    monty.end_fill()

colors = ['gold','yellow','orange','red','white']

for _ in range(15):
    x = random.randint(-250, 250)
    y = random.randint(-180, 180)
    size = random.randint(20, 100)
    c = random.choice(colors)
    star(x, y, size, c)

What Do You Think Will Happen?

The star() function draws 5 lines and turns 144° each time. 5 × 144° = 720°. That's two full rotations. Will the turtle end up facing the same direction it started? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

Yes — 720° = 2 full turns, so the turtle ends up facing exactly the same direction it started. Were you right?

How It Works

The star() function uses goto(x, y) to jump to the star's first point, then draws 5 lines of size pixels, turning 144° right after each one.

Because 5 × 144° = 720° (exactly two full circles), the last line lands the turtle back at the start facing the original direction — closing the star perfectly without any extra math.

Explanation Table

Line	What it does
def star(x, y, size, color)	Four-parameter function: position, size, and color
monty.goto(x, y)	Jump to the star's starting point
for _ in range(5)	Draw 5 points of the star
monty.right(144)	144° = the exterior angle of a 5-pointed star
random.randint(20, 100)	Random size between 20 and 100 pixels

Why 144°?

A regular pentagon has exterior angle 72°. A star skips one vertex each step, so the angle doubles: 2 × 72° = 144°. For a 6-pointed star the angle would be 2 × 60° = 120°.

Learning Check

Spot the Bug!

The program below draws shapes but they look like pentagons, not stars! Find and fix the one wrong number in the star() function.

▶ Run ↻ Reset

Change monty.right(72) to monty.right(144) — 72° draws a regular pentagon; 144° draws a star.

Experiments

1. Draw a 6-pointed star. Change range(5) to range(6) and right(144) to right(120). You'll know it worked when a Star of David shape appears.

2. Make a night sky. Add a background first: draw a large filled black rectangle before calling the star loop. You'll know it worked when the stars glow against a dark background.

3. All the same size. Change random.randint(20, 100) to a fixed 60. You'll know it worked when all stars are uniform in size but still scattered randomly.

4. Overlapping stars. Remove random.seed(7) and increase the count to range(30). Each run creates a unique star field. You'll know it worked when no two runs look the same.

Stellar Work!

You learned the 144° star trick, wrote a four-parameter function, and used random to scatter shapes across the canvas. You're thinking like a real creative coder! Up next: Traffic Light Stack — decomposing a real-world object into drawing primitives.