### 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 language | German |
---|---|

Pages (from-to) | 81-95 |

Number of pages | 15 |

Journal | Publicationes Mathematicae |

Volume | 65 |

Issue number | 1-2 |

State | Published - 2004 |

### Keywords

- Geometric construction
- Hyperbolic geometry
- Quantifier-free axiomatization

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Publicationes Mathematicae*,

*65*(1-2), 81-95.

**Fragmente der ebenen hyperbolischen Geometrie.** / Pambuccian, Victor.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 65, no. 1-2, pp. 81-95.

}

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 -