Abstract
We intend to construct these geometries using a slightly modified Hilbert’s axioms system in the same way as it is done in [36, 37, 138, 185]. An interesting thing is related to the fact that it exists as a common part for Euclidean and non-Euclidean Geometry, the so-called Absolute Geometry. Roughly speaking, the Absolute Geometry consists in all theorems that can be thought and proved using the axiomatic system before introducing a parallelism axiom.
Omnibus ex nihilo ducendis sufficit unum.
G. W. von Leibniz
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Boskoff, WG., Capozziello, S. (2024). Euclidean and Non-Euclidean Geometries: How They Appear. In: A Mathematical Journey to Relativity. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-54823-9_1
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DOI: https://doi.org/10.1007/978-3-031-54823-9_1
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