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On Angles Whose Squared Trigonometric Functions are Rational

John H. Conway·Charles Radin·Lorenzo Sadun
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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.

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John H. Conway, Charles Radin, Lorenzo Sadun. 1998-12-18. On Angles Whose Squared Trigonometric Functions are Rational. https://arxiv.org/abs/math-ph/9812019

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