On Angles Whose Squared Trigonometric Functions are Rational

Details On Angles Whose Squared Trigonometric Functions are Rational On Angles Whose Squared Trigonometric Functions are Rational

1998-12-18

arxiv.org/abs/math-ph/9812019v1

Physics

Mathematical Physics

Plain TeX. 16 pages including two embedded postscript figures

Scientific paper

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.

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