Rational Linear Combinations of Pure Geodetic Angles

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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
.
Contributed by: Izidor Hafner (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Reference
[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.
Permanent Citation
"Rational Linear Combinations of Pure Geodetic Angles"
http://demonstrations.wolfram.com/RationalLinearCombinationsOfPureGeodeticAngles/
Wolfram Demonstrations Project
Published: March 7 2011