Rational Linear Combinations of Pure Geodetic Angles

A "pure geodetic" angle is an angle with any of its six squared trigonometric functions rational (or infinite). This Demonstration shows how an angle whose tangent is of the form can be expressed as a rational linear combination of pure geodetic angles and an integral multiple of , that is, it finds rational and such that is a sum of , where and a rational linear combination of and .

[1] J. H. Conway, C. Radin, and L. Sadun, "On Angles Whose Squared Trigonometric Functions Are Rational," Discrete & Computational Geometry, 22(3), 1999 pp. 321–332.