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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Case Western Reserve University, Cleveland, OH, 44106-7058, USA

    Joel C. Langer & David A. Singer

Authors
  1. Joel C. Langer
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  2. David A. Singer
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Correspondence to Joel C. Langer.

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Langer, J.C., Singer, D.A. Reflections on the Lemniscate of Bernoulli: The Forty-Eight Faces of a Mathematical Gem. Milan J. Math. 78, 643–682 (2010). https://doi.org/10.1007/s00032-010-0124-5

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  • DOI: https://doi.org/10.1007/s00032-010-0124-5

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