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Discrete & Computational Geometry

, Volume 22, Issue 3, pp 321–332 | Cite as

On Angles Whose Squared Trigonometric Functions Are Rational

  • J. H. Conway
  • C. Radin
  • L. Sadun

Abstract.

We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, 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.

Keywords

Linear Combination Real Number Vector Space Linear Relation Trigonometric Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • J. H. Conway
    • 1
  • C. Radin
    • 2
  • L. Sadun
    • 2
  1. 1.Department of Mathematics, Princeton University, Princeton, NJ 08544, USA US
  2. 2.Department of Mathematics, University of Texas, Austin, TX 78712, USAUS

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