Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 1, pp. 165-175 (2008)

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The elementary geometry of a triangular world with hexagonal circles

Victor Pambuccian

Department of Integrative Studies, Arizona State University - West Campus, Phoenix, AZ 85069-7100, U.S.A. e-mail: pamb@math.west.asu.edu

Abstract: We provide a collinearity based elementary axiomatics of optimal quantifier complexity $\forall\exists\forall\exists$ for the geometry inside a triangle and reprove that collinearity cannot be defined in terms of segment congruence, the metric being Hilbert's projective metric.

Keywords: Hilbert geometry inside a triangle, segment congruence, collinearity, quantifier complexity

Classification (MSC2000): 51F20, 51A30, 51A45, 51G05

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Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.

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