On Angles Whose Squared Trigonometric Functions Are Rational |
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| Authors: | J. H. Conway C. Radin L. Sadun |
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| Affiliation: | (1) Department of Mathematics, Princeton University, Princeton, NJ 08544, USA , US;(2) Department of Mathematics, University of Texas, Austin, TX 78712, USA, US |
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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. Received April 7, 1998, and in revised form September 2, 1998. |
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