Symmetry and folding of continued fractions
Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 603-611

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.

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

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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/

[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. | Zbl | MR

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

[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] | Zbl | MR

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