Gauss’s 17-gon

A teenager’s discovery

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

• Gauss (1796) showed the regular 17-gon is constructible.
• An n-gon is constructible exactly when n is a power of 2 times distinct Fermat primes.
• Known Fermat primes: 3, 5, 17, 257, 65537.

Steps

1. 2,000 years of silence
2. Which can be built?
3. Counting polygons
4. The 51-gon
5. Which polygons can be built?
6. A Fermat prime