Pinwheel of Triangles

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

• Draw any regular polygon using a loop and the 360 / sides angle formula
• Repeat a shape around a center point to build radial symmetry
• Use begin_fill() and end_fill() to fill shapes with color

Draw 12 equilateral triangles, each one rotated 30° from the last. Gold and dark-red blades fan out from the center like the spokes of a spinning wheel.

Welcome to the Pinwheel of Triangles!

In this lab you'll draw one triangle at a time, rotating 30° between each one. Twelve triangles × 30° = a full 360° circle — and one stunning pinwheel! Let's code it together!

How the Pinwheel Works

Every equilateral triangle has three equal angles of 60°. To draw one with turtle graphics you turn 120° at each corner (the exterior angle — the supplement of 60°). After three sides the turtle is back exactly where it started, facing the same direction.

Then monty.right(30) spins Monty 30° clockwise before the next triangle. After 12 triangles, 12 × 30° = 360° — a full rotation — so every blade fans out evenly.

The Magic Formula

To spread n copies of any shape evenly around a center point, rotate 360 / n degrees between copies. Here n = 12, so 360 / 12 = 30. Try changing 12 to 6 or 8 and see what happens!

Sample Code

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

colors = ['gold', 'darkred']
size = 120

for i in range(12):
    monty.color(colors[i % 2])
    monty.begin_fill()
    for j in range(3):
        monty.forward(size)
        monty.left(120)
    monty.end_fill()
    monty.right(30)

monty.hideturtle()

What Do You Think Will Happen?

There are 2 colors in the list and 12 triangles to draw. How many gold triangles will appear in the finished pinwheel? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

Exactly 6 gold and 6 dark-red triangles — because i % 2 alternates 0 and 1 for each of the 12 iterations. Were you right?

How It Works

The program has two nested loops. The outer loop (for i in range(12)) repeats 12 times — once per triangle blade. The inner loop (for j in range(3)) draws the three sides of each triangle.

Inside the outer loop: - monty.color(colors[i % 2]) picks gold when i is even, dark-red when i is odd - monty.begin_fill() / monty.end_fill() sandwich the inner loop to fill the triangle solid - monty.right(30) rotates Monty 30° clockwise after each complete triangle so the next blade fans outward

The key insight is that after three forward + left(120) steps, the turtle lands exactly back at the center facing the original direction. The rotation happens between triangles, not inside them.

Explanation Table

Line	What it does
colors = ['gold', 'darkred']	Two-color list to alternate blade colors
size = 120	Side length of each triangle in pixels
for i in range(12)	Draw 12 blades — one per loop iteration
colors[i % 2]	i % 2 is 0 or 1, cycling the two colors
monty.begin_fill()	Start recording the shape to fill
for j in range(3)	Draw 3 sides — one equilateral triangle
monty.left(120)	Turn at each corner (exterior angle of equilateral triangle)
monty.end_fill()	Fill the completed triangle with the current color
monty.right(30)	Rotate 30° (= 360° ÷ 12) before the next blade

Learning Check

Your Turn — Add the Missing Rotation

The program below draws 12 triangles but they all stack on top of each other — no pinwheel! Add one line at the end of the outer loop to spread the blades evenly around the center.

▶ Run ↻ Reset

The missing line is monty.right(30) — 360° divided by 12 blades = 30° per step.

Experiments

Try these changes in the Try It Now editor above:

1. Change the number of blades. Replace range(12) with range(6) and monty.right(30) with monty.right(60). You'll know it worked when you see a 6-bladed pinwheel with wider gaps between blades.

2. Try three colors. Change colors to ['gold', 'darkred', 'navy']. With 3 colors and 12 blades, the pattern repeats every 3 blades. You'll know it worked when you see four groups of three differently colored triangles.

3. Make the blades bigger or smaller. Change size = 120 to size = 80 or size = 160. You'll know it worked when the triangles are noticeably shorter or longer.

4. Turn left instead of right between blades. Replace monty.right(30) with monty.left(30). You'll know it worked when the pinwheel looks identical — can you figure out why?

5. Draw pentagons instead of triangles. Change the inner loop to range(5) and monty.left(120) to monty.left(72). You'll know it worked when each blade is a five-sided polygon instead of a triangle.

Excellent Work!

You used the 360 / n formula, nested loops, and filled shapes to build a spinning pinwheel! The same rotation trick works for any shape — try it with squares, pentagons, or hexagons. Up next: Nested Circles to explore a completely different kind of repetition.