On Angles Whose Squared Trigonometric Functions are Rational

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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.
Plain TeX. 16 pages including two embedded postscript figures

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Mathematical Physics, Metric Geometry, Number Theory, 52B60 (Primary) 52C20, 05B45, 82B0 (Secondary)

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https://dspace.dare.co.zw/handle/123456789/90346

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arXiv

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