JOURNAL ARTICLE

Simpler foundations for the hyperbolic plane.

  • Published In: Forum Mathematicum, 2023, v. 35, n. 5. P. 1301 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Bamberg, John; Penttila, Tim 3 of 3

Abstract

H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger's axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed that hyperbolic geometry is incidence geometry. We improve upon Skala's formulation by doing away with Pappus and Desargues altogether, by substituting for them two simpler axioms. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Forum Mathematicum. 2023/09, Vol. 35, Issue 5, p1301
  • Document Type:Article
  • Subject Area:Biography
  • Publication Date:2023
  • ISSN:0933-7741
  • DOI:10.1515/forum-2022-0268
  • Accession Number:171353511
  • Copyright Statement:Copyright of Forum Mathematicum is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.