Symmetry and folding of continued fractions
Journal de théorie des nombres de Bordeaux, Volume 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.

Alfred J. Van der Poorten. Symmetry and folding of continued fractions. Journal de théorie des nombres de Bordeaux, Volume 14 (2002) no. 2, pp. 603-611. doi: 10.5802/jtnb.377
@article{JTNB_2002__14_2_603_0,
     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},
     year = {2002},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     doi = {10.5802/jtnb.377},
     zbl = {1067.11001},
     mrnumber = {2040696},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.377/}
}
TY  - JOUR
AU  - Alfred J. Van der Poorten
TI  - Symmetry and folding of continued fractions
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2002
SP  - 603
EP  - 611
VL  - 14
IS  - 2
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.377/
DO  - 10.5802/jtnb.377
LA  - en
ID  - JTNB_2002__14_2_603_0
ER  - 
%0 Journal Article
%A Alfred J. Van der Poorten
%T Symmetry and folding of continued fractions
%J Journal de théorie des nombres de Bordeaux
%D 2002
%P 603-611
%V 14
%N 2
%I Université Bordeaux I
%U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.377/
%R 10.5802/jtnb.377
%G en
%F 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. | 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

Cited by Sources: