Article

Milan Journal of Mathematics

, Volume 78, Issue 2, pp 643-682

First online:

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

  • Joel C. LangerAffiliated withDepartment of Mathematics, Case Western Reserve University Email author 
  • , David A. SingerAffiliated withDepartment of Mathematics, Case Western Reserve University

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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.