Squeezing π

Archimedes’ limit

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

• Inside and outside polygons squeeze π from both sides.
• Archimedes used 96-gons: 3 10/71 < π < 3 1/7.
• The limit of the lengths need not equal the length of the limit (the staircase paradox).

Steps

1. A hexagon inside
2. More and more sides
3. The outside hexagon
4. Archimedes’ 96-gon
5. Archimedes’ gap
6. The staircase paradox