Drawing with Circles

Spinning arrows trace any shape

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

• Circular motion is two sine waves; a sum of sines is a chain of spinning circles.
• Complex Fourier series: $z(t) = \sum c_k e^{ikt}$ draws any closed path.
• Corners need many small, fast circles; fitting with enough circles explains little by itself.

Steps

1. A point on a wheel
2. Arrows on arrows
3. Epicycles at work
4. Were the ancients wrong?
5. Drawing a square
6. Which way, how fast?