Pentagon Chain¶

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

Compute the exterior angle of any regular polygon with 360 / sides
Position shapes in a horizontal row by advancing the turtle between them
Use begin_fill() and end_fill() with two alternating colors

Ten pentagons march in a row, alternating purple and gold — a bracelet of five-sided tiles stretching across the canvas.

Welcome to the Pentagon Chain!

Monty waving welcome In this lab you'll learn the one formula that draws any regular polygon, then chain 10 of them in a row. Let's code it together!

How the Chain Works¶

A regular polygon with n sides needs an exterior angle of 360 / n degrees at each corner. For a pentagon (5 sides): 360 / 5 = 72°.

After drawing each pentagon, the turtle is back at the starting corner. Moving forward by size steps places the turtle at the next pentagon's starting corner.

Sample Code¶

import turtle
monty = turtle.Turtle()
monty.speed(0)
monty.hideturtle()

colors = ['purple', 'gold']
sides = 5
size = 60
angle = 360 / sides

monty.penup()
monty.goto(-270, 0)
monty.pendown()

for i in range(10):
    monty.color(colors[i % 2])
    monty.begin_fill()
    for _ in range(sides):
        monty.forward(size)
        monty.right(angle)
    monty.end_fill()
    monty.forward(size)

What Do You Think Will Happen?

Monty thinking The exterior angle of a pentagon is 72°. After drawing all 5 sides, how many total degrees has Monty turned? (Hint: 5 × 72° = ?) Make your guess — then click Run to find out!

Try It Now¶

5 × 72° = 360° — a complete rotation. That's why the turtle always ends up facing the same direction after any regular polygon. Were you right?

How It Works¶

The inner loop for _ in range(sides) draws one pentagon. After each side, right(angle) rotates by the exterior angle. After all 5 sides, the turtle is back at the start facing the original direction.

monty.forward(size) after end_fill() advances the turtle by exactly one side length, placing it at the first corner of the next pentagon — so the chain connects corner-to-corner.

Explanation Table¶

Line	What it does
`angle = 360 / sides`	Exterior angle formula — works for any regular polygon
`monty.goto(-270, 0)`	Start near the left edge
`for _ in range(sides)`	Draw one side + one turn, repeated `sides` times
`monty.end_fill()`	Fill the completed pentagon
`monty.forward(size)`	Advance to the next pentagon's starting corner

Learning Check¶

Your Turn — Make a Hexagon Chain

Monty thinking Change the code below to draw a chain of hexagons (6 sides) instead of pentagons. You'll need to update sides and you may want to reduce size slightly to fit 8 hexagons.

Change sides = 5 to sides = 6. The angle updates automatically to 360 / 6 = 60°.

Experiments¶

Try squares. Change sides = 4 and size = 50. Eight squares will chain across the canvas. You'll know it worked when you see a row of colored squares.
Use three colors. Change colors to ['purple', 'gold', 'crimson'] and i % 2 to i % 3. You'll know it worked when three colors cycle across the chain.
Make a vertical chain. After monty.goto(-270, 0), add monty.setheading(90). The chain will march upward. You'll know it worked when the pentagons stack vertically.
Change the number of pentagons. Replace range(10) with range(6). Adjust the starting x position so the shorter chain is still centered. You'll know it worked when 6 pentagons appear centered on the canvas.

Great Work!

Monty celebrating You mastered the exterior angle formula 360 / sides — the key to drawing any regular polygon in Python. Change one number, change the whole shape! Up next: Overlapping Squares to explore draw order and transparency effects.