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Paper folding and mathematics?

  1. Jan 8, 2006 #1
    I was reading on wikipedia when i stumbled through this article on paper folding which said:

    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. jcsd
  3. Jan 8, 2006 #2


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    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.
  4. Jan 9, 2006 #3
    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.
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