Paper by Erik D. Demaine

Reference:
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.

Abstract:
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 + n2)/2 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.

Availability:
The paper is available in PDF (218k).
See information on file formats.
[Google Scholar search]

Related papers:
AngularGrid_OSME2010 (Degenerative Coordinates in 22.5° Grid System)


See also other papers by Erik Demaine.
These pages are generated automagically from a BibTeX file.
Last updated November 24, 2020 by Erik Demaine.