Paper Folding a Hyperbola

Back in February, I learned how to use paper folding to create an ellipse. Since then, I’ve wanted to try my hand at paper folding a hyperbola as well. It’s taken a few months, but I finally did it! Previously, I have bogged about paper folding both parabolas and ellipses.

I learned about folding a hyperbola while reading More Joy of Mathematics: Exploring Mathematics All Around You by Theoni Pappas.

When I paper folded my ellipse, I started with a circle template that I printed on a sheet of paper. This worked fine because I only had to fold the edge of the circle to the dot inside the circle.

The hyperbola, on the other hand, needed a different approach because I couldn’t cut the circle out since the dot was on the outside of the circle. I decided that using wax paper would be the easiest way to construct my hyperbola.

Paper Folding a Hyperbola

Supplies:

• Wax Paper (or Patty Paper)
• Sharpie
• Circular Object to Trace Around

I used the sharpie to trace around a circular roll of tape on my wax paper.

Use the sharpie to mark a point outside the circle.

Fold the wax paper so the dot lies on the circle.

Repeat the process so the dot lands on a different part of the circle each time.

Keep folding!

You’re not done yet. Keep folding some more.

It’s a hyperbola!

I used a blue sharpie to outline the hyperbola formed by the creases.

I was pretty thrilled with how my hyperbola and ellipse turned out.

My students are currently working on a project where they are folding each of the four different conic sections using patty paper. I can’t wait to show off their work!