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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.

folded paper background with drawing of hyperbola on top

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.

paper folding ellipse from a circle conic section conics precalculus

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 folding a hyperbola conic sections

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

wax paper folding a hyperbola conic sections

Use the sharpie to mark a point outside the circle.

wax paper folding a hyperbola conic sections

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

wax paper folding a hyperbola conic sections

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

wax paper folding a hyperbola conic sections
wax paper folding a hyperbola conic sections

Keep folding!

wax paper folding a hyperbola conic sections

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

wax paper folding a hyperbola conic sections
wax paper folding a hyperbola conic sections

It’s a hyperbola!

wax paper folding a hyperbola conic sections

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

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