In the previous post on paper folding, we have learned how to use paper folding to extract the square root of a number on the number line. In this post, we are going to learn how to extract the cube root a number by paper folding. The steps in constructing the fold is very similar to extracting the square root.
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.
Exercise: Prove that if M on 
The continuation and proof of this theorem can be found here.
For GeoGebra enthusiasts, you can download the GeoGebra file here.
Reference: My old notebook. Sorry, I don’t know to whom I should attribute the paper fold.
Stumble It!
[...] 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 [...]