Barbilian spaces: the history of a geometric idea
type: Item
instance of: scholarly article
title: Barbilian spaces: the history of a geometric idea
zbMATH Open document ID: 1126.01015
author: Wladimir G. Boskoff
author: Bogdan D. Suceava
published in: Historia Mathematica
publication date: 2007-07-23T00:00:00Z
review text: Dan Barbilian (1895--1961) was both a poet and a mathematician. His mathematical papers are scarce (the article mentions 9, of which 6 are in Romanian) but one from 1934 has caught some attention. Referring to the Klein-Beltrami model of plane hyperbolic geometry, he defined in it a certain class of metric spaces, now named after him, and this article offers a ``chronological clarification'' of event which led to the recently increased interest in Barbilian's invention.
reviewed by: Roman Duda
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 51M99
zbMATH DE Number: 5173603
zbMATH Keywords: hyperbolic geometry
zbMATH Keywords: non-Euclidean geometry
zbMATH Keywords: Barbilian spaces
zbMATH Keywords: Barbilian's metrization procedure
MaRDI profile type: Publication
full work available at URL: j.hm.2006.06.001
OpenAlex ID: W1996390435
Wikidata QID: Q56553381
cites work: Zur Axiomatik der projektiven ebenen Ringgeometrien. 1. Tl
cites work: Zur Axiomatik der projektiven ebenen Ringgeometrien. 2. Tl
cites work: Q3263909
cites work: Q3266905
cites work: Q5719718
cites work: Q4379874
cites work: Q4897014
cites work: Q4324846
cites work: Q4852932
cites work: Q4366401
cites work: Q4869124
cites work: Q4706899
cites work: Q4797579
cites work: Q4764688
cites work: Q4517823
cites work: Q4439648
cites work: The Apollonian metric: limits of the comparison and bilipschitz properties
cites work: The Apollonian metric: quasi-isotropy and Seittenranta's metric
cites work: The Apollonian inner metric
cites work: The Apollonian Metric: The Comparison Property, Bilipschitz Mappings and Thick Sets
cites work: Q3432913
cites work: Isometries of the Half-Apollonian Metric
cites work: Q3446223
cites work: On the apollonian metric of domains in
cites work: Conformality of the Apollonian metric
cites work: Barbilian geometry and the Poincare Model
cites work: The non-Euclidean, hyperbolic plane. Its structure and consistency
cites work: Q4472953
DOI: 10.1016/J.HM.2006.06.001
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description: scientific article; zbMATH DE number 5173603