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.