Constant Width

Rollers that aren’t round

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

• Shapes of constant width include the circle and the Reuleaux polygons.
• Barbier: every shape of constant width w has perimeter πw.
• The Reuleaux triangle has the least area of any such shape; it can drill nearly square holes.

Steps

1. Round manhole covers
2. The Reuleaux triangle
3. Barbier’s theorem
4. Less area
5. Drilling square holes
6. Seven-sided coins