Geometry of Farey–Ford polygons

Jayadev Athreya, Sneha Chaubey, Amita Malik, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)637-656
Number of pages20
JournalNew York Journal of Mathematics
Volume21
StatePublished - 2015

Keywords

  • Distribution
  • Farey fractions
  • Ford circles

ASJC Scopus subject areas

  • Mathematics(all)

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