Paper by Erik D. Demaine
- Tomohiro Tachi and Erik D. Demaine, “Degenerative Coordinates in 22.5° Grid System”, in Origami5: Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education (OSME 2010), Singapore, July 13–17, 2010, to appear, A K Peters.
We consider the construction of points within a square of paper
by drawing a line (crease) through an existing point with angle equal to
an integer multiple of 22.5°, which is a very restricted
form of the Huzita–Justin origami construction axioms.
We show that a point can be constructed by a sequence of such operations
if and only if its coordinates are both of the form
(m + n √2)/2ℓ
for integers m, n, and ℓ ≥ 0,
and that all such points can be constructed efficiently.
This theorem explains how the restriction of angles to integer
multiples of 22.5° forces point coordinates to degenerate
into a reasonably controlled grid.
- The paper is available in PDF (218k).
- See information on file formats.
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- Related papers:
- AngularGrid_OSME2010 (Degenerative Coordinates in 22.5° Grid System)
See also other papers by Erik Demaine.
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