Folding optimal polygons from squares

Abstract : What is the largest regular n-gon that fits in a unit square? Can it be folded from a square piece of paper using standard moves from origami? Answering the first question is relatively easy, using simple ideas from geometry. The second is more interesting; our answer illustrates the difference between origami and the standard compass-and-straightedge constructions of the Greeks, where, for instance, the 7-gon cannot be constructed. Not only can we fold a 7-gon, but we can fold the largest one possible from a given square piece of paper.
The rotating caliper to design optimal bounding boxes:
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David Dureisseix. Folding optimal polygons from squares. Mathematics magazine, Mathematical Association of America, 2006, 79 (4), pp.272-280. ⟨10.2307/27642951⟩. ⟨hal-00321386⟩

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