Geometry of Farey–Ford polygons

Jayadev Athreya; Sneha Chaubey; Amita Malik; Alexandru Zaharescu

Geometry of Farey–Ford polygons

Jayadev Athreya
, Sneha Chaubey
, Amita Malik
, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 language	English (US)
Pages (from-to)	637-656
Number of pages	20
Journal	New York Journal of Mathematics
Volume	21
State	Published - 2015

All Science Journal Classification (ASJC) codes

General Mathematics

Cite this

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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.",

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year = "2015",

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pages = "637--656",

journal = "New York Journal of Mathematics",

issn = "1076-9803",

publisher = "University at Albany",

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T1 - Geometry of Farey–Ford polygons

AU - Athreya, Jayadev

AU - Chaubey, Sneha

AU - Malik, Amita

AU - Zaharescu, Alexandru

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84938564723#tab=citedBy

M3 - Article

AN - SCOPUS:84938564723

SN - 1076-9803

VL - 21

SP - 637

EP - 656

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Geometry of Farey–Ford polygons

Abstract

All Science Journal Classification (ASJC) codes

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