Skip to main content

Commentary on Menger’s Work on the Algebra of Geometry

  • Chapter
  • First Online:
  • 182 Accesses

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Wien

About this chapter

Cite this chapter

Benz, W. (2002). Commentary on Menger’s Work on the Algebra of Geometry. In: Schweizer, B., et al. Selecta Mathematica. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6110-4_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-6110-4_29

  • Published:

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-7282-7

  • Online ISBN: 978-3-7091-6110-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics