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Commentary on Menger’s Work on the Algebra of Geometry

In: Selecta Mathematica

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  • Walter Benz

Abstract

Karl Menger was one of the leading and great geometers of our Century. No doubt, much of his work in geometry must be considered as spectacular. Moreover, it initiated and substantially influenced further research in different branches of geometry. The aim of this commentary is to follow the development of his theory Algebra of Geometry, a theory which, in part, also goes under the name of Lattice-theoretic Foundations of Geometry or Geometry and Lattices. Menger was the first to present lattice-theoretic axioms in order to characterize geometrical structures [1]. This fundamental and memorable result is connected with his name in the Foundations of Geometry [2]. It also must be stressed that, although the notion of duality had long been commonplace, Menger was the first geometer to present a self-dual foundation of projective geometry.

Suggested Citation

  • Walter Benz, 2002. "Commentary on Menger’s Work on the Algebra of Geometry," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 405-416, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6110-4_29
    DOI: 10.1007/978-3-7091-6110-4_29
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