5 citations · 11 across the 15 of their papers we have counts for
4 papers · 1 filter
Necessary and sufficient conditions for convergence of integer continued fractions
Ian Short, Margaret Stanier
Fundamental to the theory of continued fractions is the fact that every infinite continued fraction with positive integer coefficients converges; however, it is unknown precisely w…
Even-integer continued fractions and the Farey tree
Ian Short, Mairi Walker
Singerman introduced to the theory of maps on surfaces an object that is a universal cover for any map. This object is a tessellation of the hyperbolic plane together with a certai…
Geodesic Rosen continued fractions
Ian Short, Mairi Walker
We describe how to represent Rosen continued fractions by paths in a class of graphs that arise naturally in hyperbolic geometry. This representation gives insight into Rosen's ori…
Ford circles, continued fractions, and best approximation of the second kind
Ian Short
We give an elementary geometric proof using Ford circles that the convergents of the continued fraction expansion of a real number coincide with the rationals that are best app…