I have looked at various ways of folding the “optimal” pentagon & hexagon (the largest regular hexagon within a square of paper). Additive constraints are a mathematically exact construction, a finite number of operations (no iterative method) and, of course, a folding sequence as simple as possible.
The goal is now to fold a regular pentagon, as large as possible, within a square of paper. In origami geometry, there exists a lot of techniques to fold an approximate pentagon. Much less are concerned with exact pentagon, and only one about optimal pentagon: R. Morassi, The elusive pentagon, in the proceedings of the First International Meeting of Origami Science and Technology, H. Huzita, editor, Ferrara, pp. 27- 37, 1989. The one proposed herein is much simple.
is the golden ratio.
2) bring C on the horizontal mid-crease.
3) bisect the complementary angle.
4) bisect again and mark the diagonal BE.
5) bisect again. I goes on J.
6) half way: B goes on J. Unfold.
7)& 8 complete the stellated pentagon.
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