98-255 John H. Conway, Charles Radin, Lorenzo Sadun

ON ANGLES WHOSE SQUARED TRIGONOMETRIC FUNCTIONS ARE RATIONAL (241K, postscript) Apr 3, 98

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Abstract. We consider the rational linear relations between real numbers whose squared trigonometric values are rational, 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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