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

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.

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Van der Poorten, Alfred J. Symmetry and folding of continued fractions. Journal de Théorie des Nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 603-611. http://www.numdam.org/item/JTNB_2002__14_2_603_0/

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[2] M. Mendès France, Sur les fractions continues limitées. Acta Arith. 23 (1973), 207-215. | MR 323727 | Zbl 0228.10007

[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 633890 | Zbl 0451.10019

[4] A.J. Van Der Poorten, J. Shallit, Folded continued fractions. J. Number Theory 40 (1992), 237-250. | MR 1149740 | Zbl 0753.11005