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Jayadev Athreya, Sneha Chaubey, Amita Malik, and Alexandru Zaharescu
Geometry of Farey-Ford polygons view print
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| Published: |
July 29, 2015 |
| Keywords: |
Ford circles, Farey fractions, distribution |
| Subject: |
37A17, 11B57, 37D40 |
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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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| Acknowledgements
J.S.A partially supported by NSF CAREER grant 1351853; NSF grant DMS 1069153; and NSF grants DMS 1107452, 1107263, 1107367 "RNMS: Geometric structures And Representation varieties" (the GEAR Network)."
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| Author information
Jayadev Athreya:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA.
jathreya@illinois.edu
Sneha Chaubey:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA.
chaubey2@illinois.edu
Amita Malik:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA.
amalik10@illinois.edu
Alexandru Zaharescu:
Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania.
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA.
zaharesc@illinois.edu
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