Adelaide Research & Scholarship
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https://hdl.handle.net/2440/137875
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| Type: | Journal article |
| Title: | Simpler foundations for the hyperbolic plane |
| Author: | Bamberg, J. Penttila, T. |
| Citation: | Forum Mathematicum, 2023; 35(5):1301-1325 |
| Publisher: | De Gruyter |
| Issue Date: | 2023 |
| ISSN: | 0933-7741 1435-5337 |
| Statement of Responsibility: | John Bamberg, Tim Penttila |
| 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. |
| Keywords: | Hyperbolic plane; metric plane; first-order axiomatisation; abstract oval |
| Description: | Published Online: 2023-03-03 |
| Rights: | © 2023 Walter de Gruyter GmbH, Berlin/Boston |
| DOI: | 10.1515/forum-2022-0268 |
| Grant ID: | http://purl.org/au-research/grants/arc/FT120100036 |
| Published version: | http://dx.doi.org/10.1515/forum-2022-0268 |
| Appears in Collections: | Mathematical Sciences publications |
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