Folding Flat

Maekawa and Kawasaki

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

• Maekawa: at each flat-folded vertex, $M - V = \pm 2$.
• Kawasaki: alternate angles around the vertex each sum to 180°.
• So interior vertices always have an even number of creases.

Steps

1. Mountains and valleys
2. Make it fold flat
3. Which will fold flat?
4. The missing angle
5. Is it foldable?
6. Count the mountains