John H. Conway, Charles Radin, Lorenzo Sadun ON ANGLES WHOSE SQUARED TRIGONOMETRIC FUNCTIONS ARE RATIONAL (241K, postscript) 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.