Milan Journal of Mathematics

, Volume 78, Issue 2, pp 643–682

Reflections on the Lemniscate of Bernoulli: The Forty-Eight Faces of a Mathematical Gem

Article

DOI: 10.1007/s00032-010-0124-5

Cite this article as:
Langer, J.C. & Singer, D.A. Milan J. Math. (2010) 78: 643. doi:10.1007/s00032-010-0124-5

Abstract

Thirteen simple closed geodesics are found in the lemniscate. Among these are nine “mirrors”—geodesics of reflection symmetry—which generate the full octahedral group and determine a triangulation of the lemniscate as a disdyakis dodecahedron. New visualizations of the lemniscate are presented.

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsCase Western Reserve UniversityClevelandUSA