Another equivalent of the Lotschnittaxiom

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We prove that Bachmann’s Lotschnittaxiom, which states that perpendiculars raised on the two legs of a right angle always meet, is equivalent, with respect to Hilbert’s plane absolute geometry, to the statement P: “For any point P, line l, with P not incident with l, and any line g, there exists a point G on g for which the distance to P exceeds the distance to l”.

Original languageEnglish (US)
Pages (from-to)167-170
Number of pages4
JournalBeitrage zur Algebra und Geometrie
Volume58
Issue number1
DOIs
StatePublished - Mar 1 2017

Keywords

  • Absolute geometry
  • Lotschnittaxiom

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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