Sphere tangency as single primitive notion for hyperbolic and Euclidean geometry. (English) Zbl 1038.51014
We have been still interested in axiomatization of elementary geometry. In this paper the author gives an axiom of \(n\)-dimensional hyperbolic geometry and Euclidean geometry in a one-sorted first-order language. The axiom he constructs is remarkable because it only starts from ‘spheres’ and ‘tangency of spheres’. This is a good work as the axiom is very plain but it is enough.
Reviewer: Kazushi Ahara (Kawasaki)
MSC:
| 51M05 | Euclidean geometries (general) and generalizations |
| 51M10 | Hyperbolic and elliptic geometries (general) and generalizations |
| 03B30 | Foundations of classical theories (including reverse mathematics) |
Keywords:
axiom; \(n\)-dimensional hyperbolic geometry; Euclidean geometry; one-sorted first-order languageReferences:
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