Trisecting with Paper

A fold can solve a cubic

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

• One origami fold can place two points onto two lines at once.
• That solves cubic equations, so folding can trisect angles and double the cube.
• Impossibility proofs depend on which tools are allowed.

Steps

1. More powerful than a compass
2. Abe’s trisection
3. Why this doesn’t break the theorem
4. What can folding construct?
5. A cubic in disguise
6. Doubling the cube