Haga’s Theorem

Thirds without measuring

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

• Folding a corner to the top edge’s midpoint divides the side into thirds (Haga).
• Landing at $t$ gives a crossing at height $\frac{t}{2 - t}$.
• Repeated folds can divide a side into any number of equal parts.

Steps

1. A biology professor’s discovery
2. Halfway up
3. Quarter landing
4. Two-thirds across
5. Folding fifths
6. Any fraction?