Fragmente der ebenen hyperbolischen Geometrie

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We provide quantifier-free axiomatizations for two fragments of hyperbolic geometry: the hyperbolic geometry of restricted ruler (which can be used to draw the line joining two distinct points, but not to construct the intersection point of two lines), segment-transporter, and set square constructions, and the geometry of BACHMANN's Treffgeradenebenen, and show that both are, in a precise sense, naturally occuring fragments of standard hyperbolic geometry.

Original languageGerman
Pages (from-to)81-95
Number of pages15
JournalPublicationes Mathematicae
Volume65
Issue number1-2
StatePublished - 2004

Keywords

  • Geometric construction
  • Hyperbolic geometry
  • Quantifier-free axiomatization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fragmente der ebenen hyperbolischen Geometrie. / Pambuccian, Victor.

In: Publicationes Mathematicae, Vol. 65, No. 1-2, 2004, p. 81-95.

Research output: Contribution to journalArticle

@article{6a2dea459baf4d08a762cf513151c390,
title = "Fragmente der ebenen hyperbolischen Geometrie",
abstract = "We provide quantifier-free axiomatizations for two fragments of hyperbolic geometry: the hyperbolic geometry of restricted ruler (which can be used to draw the line joining two distinct points, but not to construct the intersection point of two lines), segment-transporter, and set square constructions, and the geometry of BACHMANN's Treffgeradenebenen, and show that both are, in a precise sense, naturally occuring fragments of standard hyperbolic geometry.",
keywords = "Geometric construction, Hyperbolic geometry, Quantifier-free axiomatization",
author = "Victor Pambuccian",
year = "2004",
language = "German",
volume = "65",
pages = "81--95",
journal = "Publicationes Mathematicae",
issn = "0033-3883",
publisher = "Kossuth Lajos Tudomanyegyetem",
number = "1-2",

}

TY - JOUR

T1 - Fragmente der ebenen hyperbolischen Geometrie

AU - Pambuccian, Victor

PY - 2004

Y1 - 2004

N2 - We provide quantifier-free axiomatizations for two fragments of hyperbolic geometry: the hyperbolic geometry of restricted ruler (which can be used to draw the line joining two distinct points, but not to construct the intersection point of two lines), segment-transporter, and set square constructions, and the geometry of BACHMANN's Treffgeradenebenen, and show that both are, in a precise sense, naturally occuring fragments of standard hyperbolic geometry.

AB - We provide quantifier-free axiomatizations for two fragments of hyperbolic geometry: the hyperbolic geometry of restricted ruler (which can be used to draw the line joining two distinct points, but not to construct the intersection point of two lines), segment-transporter, and set square constructions, and the geometry of BACHMANN's Treffgeradenebenen, and show that both are, in a precise sense, naturally occuring fragments of standard hyperbolic geometry.

KW - Geometric construction

KW - Hyperbolic geometry

KW - Quantifier-free axiomatization

UR - http://www.scopus.com/inward/record.url?scp=4344593666&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344593666&partnerID=8YFLogxK

M3 - Article

VL - 65

SP - 81

EP - 95

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 1-2

ER -