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The Case for Absolute Geometry

In: Essays on Topology

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  • Victor Pambuccian

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

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.

Suggested Citation

  • Victor Pambuccian, 2025. "The Case for Absolute Geometry," Springer Books, in: Louis Funar & Athanase Papadopoulos (ed.), Essays on Topology, chapter 0, pages 577-591, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-81414-3_23
    DOI: 10.1007/978-3-031-81414-3_23
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