Geometry of Farey-Ford polygons
Dynamical Systems
2015-08-04 v2
Abstract
The Farey sequence is a natural exhaustion of the set of rational numbers between 0 and 1 by finite lists. Ford Circles are a natural family of mutually tangent circles associated to Farey fractions: they are an important object of study in the geometry of numbers and hyperbolic geometry. We define two sequences of polygons associated to these objects, the Euclidean and hyperbolic Farey-Ford polygons. We study the asymptotic behavior of these polygons by exploring various geometric properties such as (but not limited to) areas, length and slopes of sides, and angles between sides.
Cite
@article{arxiv.1410.4908,
title = {Geometry of Farey-Ford polygons},
author = {Jayadev Athreya and Sneha Chaubey and Amita Malik and Alexandru Zaharescu},
journal= {arXiv preprint arXiv:1410.4908},
year = {2015}
}
Comments
To appear in NYJM. http://nyjm.albany.edu/j/2015/21-28.html