Fold, paper, scissors - an exploration of origami's fold and cut problem
summary
The claim is explicit: the fold-and-cut theorem guarantees any polygonal shape can be made with a single cut. Two different proofs are sketched and a working Ruby implementation is shown that computes a straight skeleton, adds perpendicular helper folds to ensure flat foldability, and drives a live demo of paper cutting. The solver handles many shapes but struggles with extreme concavity and spiral cases due to floating‑point rounding; the implementation mostly works and suggests further refinements.
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chapters (5)
- 0:00Start
- 1:10generate any shape with 1 cut
- 5:55straight skeleton
- 6:353 edge cases
- 11:16How do we generalize
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