The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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GENERALIZED CONTINUED FRACTION ALGORITHM FOR THE INDEX 3 SUBLATTICE

  • Dong Han Kim (Department of Mathematics Education, Dongguk University)
  • Received : 2024.07.29
  • Accepted : 2024.09.20
  • Published : 2024.11.30
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Abstract

Motivated by an algorithm to generate all Pythagorean triples, Romik introduced a dynamical system on the unit circle, which corresponds the continued fraction algorithm on the index-2 sublattice. Cha et al. extended Romik's work to other ellipses and spheres and developed a dynamical system generating all Eisenstein triples. In this article, we review the dynamical systems by Romik and by Cha et al. and find connections to the continued fraction algorithms.

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Acknowledgement

Research supported by the National Research Foundation of Korea (RS-2023-00245719).

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