The Case for Absolute Geometry

Victor Pambuccian ()
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Victor Pambuccian: Arizona State University - West Campus, School of Mathematical and Natural Sciences

Chapter Chapter 23 in Essays on Topology, 2025, pp 577-591 from Springer

Abstract: Abstract This is a plea for a neglected area of geometry: absolute geometry. Among the theorems shown to hold in absolute geometry is Urquhart’s theorem, which, having been previously referred to as the most “elementary” theorem of Euclidean geometry, may henceforth be considered to be the most “elementary” theorem of absolute geometry. Prominently among the open problems mentioned is that of the existence in non-elliptic metric planes in which every segment has a midpoint of generalized centers of mass for any system of n material points with equal weights.

Keywords: Foundations of geometry; Absolute geometry; Metric planes; 01A60; 03A05; 03B30; 51-03; 51F05; 51F10; 51P05 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-81414-3_23

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DOI: 10.1007/978-3-031-81414-3_23

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