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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

한국수학교육학회지시리즈B:순수및응용수학 / 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
김동한 (동국대학교)
김동한. (2024). , 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

한국수학교육학회지시리즈B:순수및응용수학

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