Squares & Octagons

Doubling from four

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

• Two perpendicular diameters give an inscribed square, with side r√2.
• Bisecting central angles doubles the number of sides.
• Differences of constructible angles give new polygons, like the 15-gon.

Steps

1. A square in a circle
2. Side of the square
3. From square to octagon
4. Side of the octagon
5. Doubling towards π
6. Combining polygons