## Paper Folding: The proof of the cube root applet

Last week, we have discussed the second part of our Paper Folding series, a fold that extracts the cube root of any number. In this post, we are going to discuss its proof, but before that, let’s recall how to do the paper fold.

**Paper Folding Instructions **

- Get a rectangular piece of paper and fold it in the middle, horizontally and vertically, and let the creases (see green segments in the applet) represent the coordinate axes.
- Let
*M*denote (0,1) and let*R*denote (-*r*,0). - Make a single fold that places
*M*on*y*= -1 and*R*on*x=r*. - The x-intercept of the fold is .

The GeoGebra applet below visualizes the fold. Drag points

*P*and*Q*to satisfy the conditions above. Note that you can also move point*R*. » Read more