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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.

Keywords

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