TY - JOUR
T1 - Geometry of Farey–Ford polygons
AU - Athreya, Jayadev
AU - Chaubey, Sneha
AU - Malik, Amita
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© 2015, University at Albany. All rights reserved.
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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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 -