Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry

Victor Pambuccian

doi:10.1515/form.2003.047

Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry

Victor Pambuccian

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We show that both elementary n-dimensional hyperbolic geometry and Euclidean geometry (for all n ≥: 2) can be axiomatized in a one-sorted first-order language with spheres as individual variables and the binary predicate of sphere tangency as the only primitive notion.

Original language	English (US)
Pages (from-to)	943-947
Number of pages	5
Journal	Forum Mathematicum
Volume	15
Issue number	6
DOIs	https://doi.org/10.1515/form.2003.047
State	Published - 2003

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1515/form.2003.047

Cite this

@article{46eeecf8bc0c4a55b885412f4309f37f,

title = "Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry",

abstract = "We show that both elementary n-dimensional hyperbolic geometry and Euclidean geometry (for all n ≥: 2) can be axiomatized in a one-sorted first-order language with spheres as individual variables and the binary predicate of sphere tangency as the only primitive notion.",

author = "Victor Pambuccian",

year = "2003",

doi = "10.1515/form.2003.047",

language = "English (US)",

volume = "15",

pages = "943--947",

journal = "Forum Mathematicum",

issn = "0933-7741",

publisher = "Walter de Gruyter GmbH & Co. KG",

number = "6",

}

TY - JOUR

T1 - Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry

AU - Pambuccian, Victor

PY - 2003

Y1 - 2003

N2 - We show that both elementary n-dimensional hyperbolic geometry and Euclidean geometry (for all n ≥: 2) can be axiomatized in a one-sorted first-order language with spheres as individual variables and the binary predicate of sphere tangency as the only primitive notion.

AB - We show that both elementary n-dimensional hyperbolic geometry and Euclidean geometry (for all n ≥: 2) can be axiomatized in a one-sorted first-order language with spheres as individual variables and the binary predicate of sphere tangency as the only primitive notion.

UR - http://www.scopus.com/inward/record.url?scp=0242350392&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242350392&partnerID=8YFLogxK

U2 - 10.1515/form.2003.047

DO - 10.1515/form.2003.047

M3 - Article

AN - SCOPUS:0242350392

SN - 0933-7741

VL - 15

SP - 943

EP - 947

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 6

ER -

Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this