Rational Linear Combinations of Pure Geodetic Angles, Part 2

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A "pure geodetic" angle is an angle such that any of the six squared trigonometric functions of
is 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 a rational linear combination of
,
,
, and
plus an integer multiple of
.
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, Part 2"
http://demonstrations.wolfram.com/RationalLinearCombinationsOfPureGeodeticAnglesPart2/
Wolfram Demonstrations Project
Published: March 7 2011