Rational Linear Combinations of Pure Geodetic Angles, Part 2

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send