Simpler foundations for the hyperbolic plane

John Bamberg, Tim Penttila

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1301-1325
Number of pages25
JournalForum Mathematicum
Issue number5
Publication statusPublished - 1 Sept 2023


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