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

Access to Document

10.4171/EM/228

http://dx.doi.org/10.4171/EM/228

Fingerprint Dive into the research topics of 'On the Möbius geometry of Euclidean triangles'. Together they form a unique fingerprint.

Cite this

@article{ac8c790a7c8a4613892e10ea1f0a0d89,

title = "On the M{\"o}bius geometry of Euclidean triangles",

abstract = "We study the geometry of a Euclidean triangle from a M{\"o}bius geometric point of view. It turns out that its in- and ex-centers can be constructed in a symmetric and M{\"o}bius 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.",

author = "Udo Hertrich-Jeromin and Alastair King and Jun O'Hara",

year = "2013",

doi = "10.4171/EM/228",

language = "English",

volume = "68",

pages = "96--114",

journal = "Elemente der Mathematik",

issn = "0013-6018",

number = "3",

}

TY - JOUR

T1 - On the Möbius geometry of Euclidean triangles

AU - Hertrich-Jeromin, Udo

AU - King, Alastair

AU - O'Hara, Jun

PY - 2013

Y1 - 2013

N2 - 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.

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.

UR - http://dx.doi.org/10.4171/EM/228

U2 - 10.4171/EM/228

DO - 10.4171/EM/228

M3 - Article

VL - 68

SP - 96

EP - 114

JO - Elemente der Mathematik

JF - Elemente der Mathematik

SN - 0013-6018

IS - 3

ER -