Is Parallel Postulate Necessary?
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916703056691200 |
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| author | Wang, Chengpu Wang, Alice |
| author_facet | Wang, Chengpu Wang, Alice |
| contents | As a much later addition to the original Euclidean geometry, the parallel postulate distinguishes non-Euclidean geometries from Euclidean geometry. This paper will show that the parallel postulate is unnecessary because the 4th Euclidean axiom can already achieve the same goal. Furthermore, using the 4th Euclidean axiom can measure space curvature locally on manifold, while using the parallel postulate cannot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Is Parallel Postulate Necessary? Wang, Chengpu Wang, Alice Logic 51F99 G.0 As a much later addition to the original Euclidean geometry, the parallel postulate distinguishes non-Euclidean geometries from Euclidean geometry. This paper will show that the parallel postulate is unnecessary because the 4th Euclidean axiom can already achieve the same goal. Furthermore, using the 4th Euclidean axiom can measure space curvature locally on manifold, while using the parallel postulate cannot. |
| title | Is Parallel Postulate Necessary? |
| topic | Logic 51F99 G.0 |
| url | https://arxiv.org/abs/2303.11333 |