Folding optimal polygons from squares

David Dureisseix (1)

1 UM2 - Université Montpellier 2 - Sciences et Techniques

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:

Domaines: Géométrie métrique [math.MG]; Histoire et perspectives sur les mathématiques [math.HO]

David Dureisseix. Folding optimal polygons from squares. Mathematics magazine, 2006, 79 (4), pp.272-280. ⟨10.2307/27642951⟩. ⟨hal-00321386⟩