On M. T. Calapso's characterization of the metric of an absolute plane
type: Item
instance of: scholarly article
title: On M. T. Calapso's characterization of the metric of an absolute plane
zbMATH Open document ID: 1169.51017
author: Victor V. Pambuccian
author: Rolf Struve
published in: Journal of Geometry
publication date: 2009-06-08T00:00:00Z
review text: The authors describe the importance of M. T. Calapso's axiom for the axiomatization of hyperbolic planes by means of the midpoint relation alone and also for the axiomatization of metric planes. They show the equivalence between Calapso's axiom and the rectangle existence axiom under two fairly weak axiom systems, one is a fragment of an axiom system proposed by K. Sörensen for nonelliptic metric planes, the second is the axiom system for Wolff planes.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 51F05
Mathematics Subject Classification ID: 51F20
Mathematics Subject Classification ID: 51M05
zbMATH DE Number: 5562636
zbMATH Keywords: absolute plane
zbMATH Keywords: plane with congruence
zbMATH Keywords: metric plane
zbMATH Keywords: Wolff plane
zbMATH Keywords: Euclidean metric
zbMATH Keywords: rectangle axiom
MaRDI profile type: Publication
full work available at URL: s00022-008-2034-z
OpenAlex ID: W2038108736
DOI: 10.1007/S00022-008-2034-Z
description: scientific article; zbMATH DE number 5562636