# Paper folding and mathematics?

1. Jan 8, 2006

### ebola_virus

Paper folds can be constructed to solve square roots and cube roots; fourth-degree polynomial equations can also be solved by paper folds. The full scope of paper-folding-constructible algebraic numbers (e.g. whether it encompasses fifth or higher degree polynomial roots) remains unknown.

fascinated, i started looking for what they meant by this; are they really saying you can solve z^5 = 1 just by paper fodling? then again, i couldn't find any resources on this notion. could anyone care to explain? thanks again

2. Jan 8, 2006

### Hurkyl

Staff Emeritus
If I remember correctly, paper folding can do anything that a straightedge and compass can do. (and more, of course) (Well, I mean it can find any point and any line that can be found with straightedge and compass. Of course, I can't draw a circle with paper folding)

I can solve z^5 = 1 with a straightedge and compass, so I can solve that with paper folding too. :tongue2:

What they're saying is that it is unknown if paper folding can find roots for all 5-th degree polynomials.

3. Jan 9, 2006

### Doodle Bob

Although I haven't read the papers too extensively, I actually thought that this was settled by Roger Alperin's work back in 2000 published in the New York Journal of Mathematics.