5 Citations (Scopus)

Abstract

We provide ∀∃-axiom systems for two variants of plane equiaffine geometry, one whose automorphisms are area preserving affinities, the other whose automorphisms are oriented area preserving affinities. The axiom systems are formulated in first order languages with points as the only individual variables, and a single ternary primitive notion, standing for 'triangle of fixed (oriented or non-oriented) area'. The theorem of G. Martin on area preserving bijections of the plane is seen in a new light.

Original languageEnglish (US)
Pages (from-to)90-99
Number of pages10
JournalAequationes Mathematicae
Volume66
Issue number1-2
DOIs
StatePublished - Aug 2003

Fingerprint

Geometry
Axiom
Affine transformation
Automorphisms
Bijection
Ternary
Triangle
First-order
Theorem
Language

Keywords

  • Axiom system
  • Definability
  • Plane equiaffine geometry

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

What is plane equiaffine geometry? / Pambuccian, Victor.

In: Aequationes Mathematicae, Vol. 66, No. 1-2, 08.2003, p. 90-99.

Research output: Contribution to journalArticle

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