The Pons Asinorum for Tetrahedra
| العنوان: | The Pons Asinorum for Tetrahedra |
|---|---|
| المؤلفون: | Mowaffaq Hajja |
| المصدر: | Journal of Geometry. 93:71-82 |
| بيانات النشر: | Springer Science and Business Media LLC, 2009. |
| سنة النشر: | 2009 |
| مصطلحات موضوعية: | Combinatorics, Statement (logic), Generalization, Pons asinorum, Converse, Tetrahedron, Geometry, Proposition, Geometry and Topology, State (functional analysis), Mathematics |
| الوصف: | Proposition 5 of Book I of Euclid’s Elements, better known as the Pons Asinorum or the Asses’ Bridge, and its converse, Proposition 6, state that two sides of a triangle are equal if and only if the opposite angles are equal. A generalization of this statement to higher dimensional d-simplices is considered in [14], where it is shown that such a generalization holds only if the underlying d-simplex is orthocentric. In this paper, it is shown that a reasonably satisfactory generalization holds for all, not necessarily orthocentric, tetrahedra. It is also shown that a stronger statement than that given in [14] holds for orthocentric tetrahedra. |
| تدمد: | 1420-8997 0047-2468 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::9f97cb2aa6d86df3f934cf5d0a13e2a3 https://doi.org/10.1007/s00022-009-1972-4 |
| حقوق: | CLOSED |
| رقم الأكسشن: | edsair.doi...........9f97cb2aa6d86df3f934cf5d0a13e2a3 |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 14208997 00472468 |
|---|