[On the determination of the perimeter of the eight-centered oval]
This note aims to present the history of the main researches carried out to represent an ellipse by means of an eight-centered oval and to complete them by giving a geometrical demonstration of the formulas expressing the coordinates of the centers, the radii and the central angles of these arcs of circles making up this oval. These formulas will make it possible to determine its perimeter and thus to approximate the value of that of the ellipse. This result could be useful for archaeologists, who will test the hypothesis according to which some Roman amphitheatres, such as the Coliseum, were built from eight-centered ovals.
L'objet de cette note est de présenter l'histoire des principales recherches réalisées pour représenter une ellipse au moyen d'un ovale à huit centres et de les compléter en donnant une démonstration géométrique des formules exprimant les coordonnées des centres, des rayons et des angles aux centres des arcs de cercle constituant cet ovale. Ces formules permettront de déterminer son périmètre et donc d'approximer la valeur de celui de l'ellipse. Ce résultat pourrait s'avérer utile pour les archéologues, qui vérifieront ainsi l'hypothèse selon laquelle certains amphithéâtres romains, comme le Colisée, ont bien été construits à partir d'ovales à huit centres.
Accepted:
Published online:
Jean-Marc Ginoux 1; Jean-Claude Golvin 2
@article{CRMATH_2018__356_11-12_1195_0, author = {Jean-Marc Ginoux and Jean-Claude Golvin}, title = {Sur la d\'etermination du p\'erim\`etre de l'ovale \`a huit centres}, journal = {Comptes Rendus. Math\'ematique}, pages = {1195--1202}, publisher = {Elsevier}, volume = {356}, number = {11-12}, year = {2018}, doi = {10.1016/j.crma.2018.10.009}, language = {fr}, }
Jean-Marc Ginoux; Jean-Claude Golvin. Sur la détermination du périmètre de l'ovale à huit centres. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1195-1202. doi : 10.1016/j.crma.2018.10.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.10.009/
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