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Two posts by Evelyn Lamb about the theorem that you can make any shape by folding+one cut, and a fold+cut alphabet by Erik and Marty Demaine and Katie Steckles: blogs.scientificamerican.com/r and blogs.scientificamerican.com/r

Small peeve: Lamb and Steckles omit credit for some theorem authors, particularly Lubiw.

If you want to design your own, the disk packing method is implemented at jorigami.sourceforge.net/ but I think the straight skeleton method produces prettier folding patterns.

@11011110 I have a different peeve: E. Demaine, M. Demaine, and Lubiw didn't actually prove the Fold and Cut theorem! Their straight-skeleton-based algorithm doesn't necessarily yield a finite number of folds, thanks to the possibility of "dense spiraling". (See Figure 17.10 in Geometric Folding Algorithms.) The first actual *proof* is your circle-packing argument with Bern, E. Demaine, and Hayes (1998), with some bugs corrected by E. Demaine and O'Rourke in (2006).

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