Hexagons & Pentagons

Stepping around a circle

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Stepping the radius around a circle six times gives a regular hexagon.
• Bisecting arcs doubles the number of sides.
• The pentagon is constructible because its diagonal-to-side ratio $\frac{1+\sqrt5}{2}$ uses only a square root.

Steps

1. Walk the compass
2. More sides
3. The pentagon
4. Ptolemy’s pentagon
5. The golden diagonal
6. Perimeter of a hexagon
7. Archimedes’ first step