Folding a Parabola

Creases that solve equations

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 point onto a line gives a crease tangent to a parabola.
• A crease through a given point solves a quadratic equation.
• Beloch’s fold solves cubics, which is why origami can trisect angles.

Steps

1. Point onto line
2. Why a parabola?
3. Many folds
4. A crease through a point
5. How many creases?
6. Where it touches