The altitudes of a triangle
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911818725720064 |
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| author | Mandelkern, Mark |
| author_facet | Mandelkern, Mark |
| contents | A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a remarkable number of proofs have been put forward; this suggests a search for the most elementary and direct proof. This paper provides a simple, direct, elementary proof of the theorem; it is based solely on the Elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The altitudes of a triangle Mandelkern, Mark History and Overview Primary 51M04 A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a remarkable number of proofs have been put forward; this suggests a search for the most elementary and direct proof. This paper provides a simple, direct, elementary proof of the theorem; it is based solely on the Elements. |
| title | The altitudes of a triangle |
| topic | History and Overview Primary 51M04 |
| url | https://arxiv.org/abs/2403.19670 |