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Fold & Cut Theorem: Cut any shape from only one cut

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Can you cut a square from the center of a piece of paper with just one straight cut? Spoiler: YES, you can. In this Numberphile video, Manchester-based mathematician Dr. Katie Steckles demonstrates an idea that dates back to 1721 in Japan: The Fold and Cut Theorem. It states that “any shape with straight sides can be cut from a single (idealized) sheet of paper by folding it flat and making a single straight complete cut.” Any polygon, just one snip.

Stars? Yes. Jackolanterns? Yes. All 26 letters of the alphabet? Dr. Steckles demonstrates that! Plus, be sure to check out these DIY printable examples at ErikDemaine.org/foldcut, and/or try making up a few on your own.

fold and cut theorem
File under: origami, paper cutting, and math.

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