Another equivalent of the Lotschnittaxiom

Victor Pambuccian

doi:10.1007/s13366-016-0307-5

Another equivalent of the Lotschnittaxiom

Victor Pambuccian

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

4 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 language	English (US)
Pages (from-to)	167-170
Number of pages	4
Journal	Beitrage zur Algebra und Geometrie
Volume	58
Issue number	1
DOIs	https://doi.org/10.1007/s13366-016-0307-5
State	Published - Mar 1 2017

Keywords

Absolute geometry
Lotschnittaxiom

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s13366-016-0307-5

Cite this

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AB - 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”.

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Another equivalent of the Lotschnittaxiom

Abstract

Keywords

ASJC Scopus subject areas

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