4 Citations (Scopus)

Abstract

On the basis of the theory ε- of Pasch-free 2-dimensional geometry, Pasch's axiom is shown to be equivalent to the conjunction of the following two axioms: "In any right triangle the hypotenuse is greater than the leg" and "If ∠AOB is right, B lies between O and C, and D is the footpoint of the perpendicular from B to AC, then the segment OA is greater than the segment BD." This represents an attempt to split the Pasch axiom with respect to ε-. Only the question whether the second of the above two axioms is really weaker than Pasch's axiom, remains open.

Original languageEnglish (US)
Pages (from-to)126-130
Number of pages5
JournalJournal of Geometry
Volume56
Issue number1-2
StatePublished - 1996

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Axiom
Axioms
Hypotenuse
Right-angled triangle
Perpendicular

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Splitting the pasch axiom. / Pambuccian, Victor.

In: Journal of Geometry, Vol. 56, No. 1-2, 1996, p. 126-130.

Research output: Contribution to journalArticle

Pambuccian, V 1996, 'Splitting the pasch axiom', Journal of Geometry, vol. 56, no. 1-2, pp. 126-130.
Pambuccian, Victor. / Splitting the pasch axiom. In: Journal of Geometry. 1996 ; Vol. 56, No. 1-2. pp. 126-130.
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