On Angles Whose Squared Trigonometric Functions are Rational
Mathematical Physics
2007-05-23 v1 Metric Geometry
math.MP
Number Theory
Abstract
We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call ``geodetic''. We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles and rational linear combinations of geodetic angles appear naturally in Euclidean geometry; for illustration we apply our results to equidecomposability of polyhedra.
Cite
@article{arxiv.math-ph/9812019,
title = {On Angles Whose Squared Trigonometric Functions are Rational},
author = {John H. Conway and Charles Radin and Lorenzo Sadun},
journal= {arXiv preprint arXiv:math-ph/9812019},
year = {2007}
}
Comments
Plain TeX. 16 pages including two embedded postscript figures