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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.31 No.4

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Generalized Continued Fraction Algorithm for the Index 3 Sublattice

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2024, v.31 no.4, pp.439-451
https://doi.org/10.7468/jksmeb.2024.31.4.439
Kim Dong Han (Dongguk University)
Kim, D. H. (2024). Generalized Continued Fraction Algorithm for the Index 3 Sublattice, 31(4), 439-451, https://doi.org/10.7468/jksmeb.2024.31.4.439

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.

keywords
continued fraction, even continued fraction, Romik’s dynamical system, Diophantine approximation on the circle, index-3 sublattice

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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