Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 1, pp. 165175 (2008) 

The elementary geometry of a triangular world with hexagonal circlesVictor PambuccianDepartment of Integrative Studies, Arizona State University  West Campus, Phoenix, AZ 850697100, U.S.A. email: pamb@math.west.asu.eduAbstract: 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 Full text of the article:
Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.
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