Spirographs

Gears rolling inside rings

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A spirograph traces a hypotrochoid: a circle rolling inside a circle.
• Points = R ÷ gcd(R, g); trips round the ring = g ÷ gcd(R, g).
• A half-size gear draws straight lines (the Tusi couple).

Steps

1. A gear inside a ring
2. Counting the points
3. A five-pointed pattern
4. A bigger ring
5. Half-size gear
6. Sharp corners