**Reference**:- Tomohiro Tachi and Erik D. Demaine, “Degenerative Coordinates in 22.5° Grid System”, in
*Origami*, Singapore, July 13–17, 2010, to appear, A K Peters.^{5}: Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education (OSME 2010) **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*+*n*√2)/2^{ℓ}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.

Last updated June 1, 2023 by Erik Demaine.