Mappings preserving the area equality of hyperbolic triangles are motions

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

It is shown that a mapping φ: U → B between models U and B of elementary plane hyperbolic geometry, coordinatized by Euclidean ordered fields, that maps triangles having the same area and sharing a side into triangles that have the same property, must be a hyperbolic motion onto φ(U). The relations that Tarski and Szmielew used as primitives for geometry, the equidistance relation ≡ and the betweenness relation B are shown to be positively existentially definable in terms of the quaternary relation Δ, with Δ(abcd) standing for "the triangles abc and abd have the same area."

Original languageEnglish (US)
Pages (from-to)293-300
Number of pages8
JournalArchiv der Mathematik
Volume95
Issue number3
DOIs
StatePublished - Jul 20 2010

Keywords

  • Hyperbolic motions
  • Hyperbolic plane
  • Triangle area

ASJC Scopus subject areas

  • Mathematics(all)

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