Courbes, courbes elliptiques - Curves, elliptic curves

Robert Ferréol

Alexandre Mathieu, Timo Ogliastri, Benjamin Roadley, ece École Centrale d'Électronique

Courbes de Koch, Bézier, Cramer, Lamé, Lissajous. Lemniscate de Bernoulli. Spirales de Bernoulli, Archimède, Fermat

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The original purpose of the ECMNET project was to make Richard's prediction true, i.e. to find a factor of 50 digits or more by ECM. This goal was attained on September 14, 1998, when Conrad Curry found a 53-digit factor of 2^677-1 c150 using George Woltman's mprime program. The new goal of ECMNET is now to find other large factors by ecm, mainly by contributing to the Cunningham project, most likely the longest, ongoing computational project in history according to Bob Silverman. A new record was set by Nik Lygeros and Michel Mizony, who found in December 1999 a prime factor of 54 digits using GMP-ECM.

Rapport de recherche de l'INRIA Kostov, V.P. - Degtiariova-Kostova, E.V.

Une clothoïde (ou spirale de Cornu) est une courbe plane dont la courbure est une fonction linéaire de sa longueur.