Symmetry and folding of continued fractions

Alfred J. Van der Poorten

Alfred J. Van der Poorten

Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 603-611.

Résumé
Abstract

Le «lemme de pliage» de Michel Mendès France fournit une nouvelle justification de la symétrie du développement en fraction continue d'un irrationnel quadratique.

Michel Mendès France's “Folding Lemma” for continued fraction expansions provides an unusual explanation for the well known symmetry in the expansion of a quadratic irrational integer.

MR Zbl

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     author = {Alfred J. Van der Poorten},
     title = {Symmetry and folding of continued fractions},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {603--611},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     year = {2002},
     zbl = {1067.11001},
     mrnumber = {2040696},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2002__14_2_603_0/}
}

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Alfred J. Van der Poorten. Symmetry and folding of continued fractions. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 603-611. https://jtnb.centre-mersenne.org/item/JTNB_2002__14_2_603_0/

Bibliographie
Cité par

[1] F.M. Dekking, M. Mendès France, A.J. Van Der Poorten, FOLDS!. Math. Intelligencer 4 (1982), 130-138; II: Symmetry disturbed. ibid. 173-181; III: More morphisms. ibid. 190-195. Erratum 5 (1983), page 5. | MR | Zbl

[2] M. Mendès France, Sur les fractions continues limitées. Acta Arith. 23 (1973), 207-215. | MR | Zbl

[3] M. Mendès France, Principe de la symétrie perturbée. Seminar on Number Theory, Paris 1979-80, 77-98, Progr. Math. 12, Birkhäuser, Boston, Mass., 1981. [MR 83a:10089] | MR | Zbl

[4] A.J. Van Der Poorten, J. Shallit, Folded continued fractions. J. Number Theory 40 (1992), 237-250. | MR | Zbl