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Hyperbolic geometry and the Hillam-Thron theorem

Short, Ian (2006). Hyperbolic geometry and the Hillam-Thron theorem. Geometriae Dedicata, 119(1) pp. 91–104.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/s10711-006-9053-4
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Abstract

Every open ball within $\mathbb{R}\frac{N}{\infty}$ has an associated hyperbolic metric and Möbius transformations act as hyperbolic isometries from one ball to another. The Hillam–Thron Theorem is concerned with images of balls under Möbius transformation, yet existing proofs of the theorem do not make use of hyperbolic geometry. We exploit hyperbolic geometry in proving a generalisation of the Hillam–Thron Theorem and examine the precise configurations of points and balls that arise in that theorem.

Item Type: Journal Article
Copyright Holders: 2006 Springer Science+Business Media, Inc.
ISSN: 0046-5755
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetScience Foundation Ireland grant 05/RFP/MAT0003
Keywords: continued fractions; hyperbolic geometry
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22451
Depositing User: Ian Short
Date Deposited: 28 Jul 2010 11:14
Last Modified: 30 Mar 2011 04:09
URI: http://oro.open.ac.uk/id/eprint/22451
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