Continued Fractions

Some (mostly on-line) resources

__Books:__

- O. Karpenkov, Geometry of continued Fractions, Springer,2013 ( library link).
- G. H. Hardy, E. M. Wright, An introduction to the theory of numbers, Oxford : Clarendon Press, 1979( library link).
- A. Hatcher, Topology of numbers, unpublished draft.

__Lecture notes:__

- O. Karpenkov, Continued Fractions and Generalizations Lecture notes, TU Graz, 2011.
- W. F. Hammond, Continued Fractions and the Euclidean Algorithm. Lecture notes, University at Albany, 1997.
- G. G. Krishnan, Continued Fractions. Lecture notes, Cornell University, 2016.

__Introductory papers:__

- Caroline Series, The Geometry of Markoff Numbers.
- C. Series,
__Continued fractions and hyperbolic geometry__. - M. C. Irwin,
__Geometry of continued fractions__. - I. Richards,
__Continued frections without tears__. - J. Barrow,
__Chaos in Numberland: The secret life of continued fractions__.

__Presentations:__

- A. Leonardis,
__Simple applications of Continued Fractions and an elementary result on Heronâ€™s algorithm__. - M. Walker,
__Continued fractions and hyperbolic geometry__. - M. Waldschmid,
__Continued fractions: introduction and applications__. - A. Veselov,
__Arithmetic and geometry of Conway river__. - I. Short,
__Geodesic continued fractions__. See also__other presentations__by Ian Short.

__Webpages:__

- R. Knott,
__Continued fractions__. ---- - Y. Grabovsky,
__If Pope Gregory new continued fractions__. ----

__Some recent results:__

- I. Short, M. Walker
__Even-integer continued fractions and the Farey tree__. - I. Canakci, R. Schiffler
__Snake graphs and continued fractions__. - L. H. Kauffman and S. Lambropoulou
__From tangle frections to DNA__. - K. Spalding, A. Veselov,
__Conway river and Arnold sail__. - V. Ovsienko,
__Partitions of unity in SL(2,Z), negative continued fractions, and dissections of polygons__. - O. Karpenkov,
__Continued Fraction approach to Gauss Reduction Theory__. - O. Karpenkov,
__On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups__.

__More papers:__