Pi, Archimedes and circular splines
Résumé
In the present paper, we give approximate values of $\pi$ deduced from the areas of inscribed and circumscribed quadratic and cubic circular splines. Similar results on circular splines of higher degrees and higher approximation orders can be obtained in the same way. We compare these values to those obtained by computing the {\em perimeters} of those circular splines. We observe that the former are much easier to compute than the latter and give results of the same order. It also appears that Richardson extrapolation is very efficient on sequences of areas and give very good approximations of $\pi$. Finally, we also consider circular curves obtained by two subdivision algorithms.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)
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