On the Möbius geometry of Euclidean triangles

Udo Hertrich-Jeromin; Alastair King; Jun O'Hara

doi:10.4171/EM/228

On the Möbius geometry of Euclidean triangles

Udo Hertrich-Jeromin, Alastair King, Jun O'Hara

Department of Mathematical Sciences

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

Abstract

We study the geometry of a Euclidean triangle from a Möbius geometric point of view. It turns out that its in- and ex-centers can be constructed in a symmetric and Möbius invariant way. We relate this construction to Thurston's center of symmetry of an ideal tetrahedron in hyperbolic space and discuss some implications for the Euclidean triangle.

Original language	English
Pages (from-to)	96-114
Journal	Elemente der Mathematik
Volume	68
Issue number	3
DOIs	https://doi.org/10.4171/EM/228
Publication status	Published - 2013

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10.4171/EM/228

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AB - We study the geometry of a Euclidean triangle from a Möbius geometric point of view. It turns out that its in- and ex-centers can be constructed in a symmetric and Möbius invariant way. We relate this construction to Thurston's center of symmetry of an ideal tetrahedron in hyperbolic space and discuss some implications for the Euclidean triangle.

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U2 - 10.4171/EM/228

DO - 10.4171/EM/228

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JO - Elemente der Mathematik

JF - Elemente der Mathematik

SN - 0013-6018

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On the Möbius geometry of Euclidean triangles

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