From Euclidean triangles to the hyperbolic plane
| dc.authorid | Saglam, Ismail/0000-0002-1283-6396 | |
| dc.contributor.author | Saglam, Ismail | |
| dc.date.accessioned | 2025-01-06T17:37:46Z | |
| dc.date.available | 2025-01-06T17:37:46Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | We introduce a model of the hyperbolic plane which arises from Thurston's ideas on best Lipschitz maps between surfaces. More precisely, we apply Thurston's theory to the space of Euclidean triangles. We prove that the Lipschitz constant of the unique affine map between two Euclidean triangles induces a metric on the set of isometry classes of the triangles with area 1/2. We then prove that this space of triangles together with 2 times its natural metric is isometric to the hyperbolic plane. Our construction is simple and natural and it makes relations between several geometrical ideas. (C) 2021 Elsevier GmbH. All rights reserved. | |
| dc.description.sponsorship | TUBIITAK, Turkey | |
| dc.description.sponsorship | The question addressed in the present paper is suggested by Athanase Papadopoulos. The author is grateful to him for his remarks and comments. This work is supported by TUBIITAK, Turkey. | |
| dc.identifier.doi | 10.1016/j.exmath.2021.10.003 | |
| dc.identifier.endpage | 253 | |
| dc.identifier.issn | 0723-0869 | |
| dc.identifier.issn | 1878-0792 | |
| dc.identifier.issue | 2 | |
| dc.identifier.scopus | 2-s2.0-85119607903 | |
| dc.identifier.scopusquality | Q3 | |
| dc.identifier.startpage | 249 | |
| dc.identifier.uri | https://doi.org/10.1016/j.exmath.2021.10.003 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14669/2345 | |
| dc.identifier.volume | 40 | |
| dc.identifier.wos | WOS:000809967600003 | |
| dc.identifier.wosquality | Q3 | |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | |
| dc.publisher | Elsevier Gmbh | |
| dc.relation.ispartof | Expositiones Mathematicae | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.snmz | KA_20241211 | |
| dc.subject | Euclidean triangles | |
| dc.subject | Lipschitz maps | |
| dc.subject | Hyperbolic plane | |
| dc.title | From Euclidean triangles to the hyperbolic plane | |
| dc.type | Article |
