The 'form' of a triangle
| Autor: | Alain Chenciner |
|---|---|
| Jazyk: | English<br />French<br />Italian |
| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Rendiconti di Matematica e delle Sue Applicazioni, Vol 27, Iss 1, Pp 1-16 (2007) |
| Druh dokumentu: | article |
| ISSN: | 1120-7183 2532-3350 |
| Popis: | Heron’s formula, maybe due to Archimedes, expresses the squared area of a triangle as a polynomial in the squared lengths of its sides. A true understanding of this formula comes from an adequate coding of the shape of a triangle, i.e. of the triangle up to translations, rotations and reflexions. One can then build a “space of triangle shapes” which, if orientation is added becomes the “shape sphere” and possesses very nice symmetries which were recently used in researches on the 3-body problem. The invariant interpretation of the shape sphere in turn sheds light on the nature of Heron’s formula. |
| Databáze: | Directory of Open Access Journals |
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