Sur la détermination du périmètre de l'ovale à huit centres

Abstract : On the perimeter length determination of the eight-centered oval. Several studies have shown that an eight-centered oval coincides almost perfectly with the ellipse constructed on the same axes and can be considered as a representation of the latter provided that the radii of the arcs of circles that compose it had been suitably chosen. Its perimeter's computation is then reduced to the simple sum of arc lengths of circles. However, it does not seem to us that this calculation, which could prove to be useful, has never been performed nor published. This note aims thus to present a geometric demonstration of the perimeter length determination of the eight-centered oval.
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Jean-Marc Ginoux, Jean-Claude Golvin. Sur la détermination du périmètre de l'ovale à huit centres. Comptes Rendus Mathématique, Elsevier Masson, 2018, 356 (11-12), pp.1195-1202. ⟨10.1016/j.crma.2018.10.009⟩. ⟨hal-02196055⟩

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