Three Famous Problems

Doubling, trisecting and squaring

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

• Doubling the cube needs $\sqrt[3]{2}$: impossible (Wantzel, 1837).
• General angle trisection is impossible, though some angles can be trisected.
• Squaring the circle needs $\sqrt\pi$, and $\pi$ is transcendental (Lindemann, 1882).

Steps

1. The three classical problems
2. The Delian problem
3. But I can trisect 90°!
4. Why not 60°?
5. Doubling the altar
6. Squaring the circle