Discrete & Computational Geometry

, Volume 22, Issue 3, pp 321–332

On Angles Whose Squared Trigonometric Functions Are Rational

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

DOI: 10.1007/PL00009463

Cite this article as:
Conway, J., Radin, C. & Sadun, L. Discrete Comput Geom (1999) 22: 321. doi:10.1007/PL00009463

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.

Copyright information

© 1998 Springer-Verlag New York Inc.

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