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UID:6763@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20200402T140000
DTEND;TZID=Europe/Paris:20200402T150000
DTSTAMP:20250118T133331Z
URL:https://www.i2m.univ-amu.fr/evenements/jean-paul-brasselet-une-demonst
 ration-elementaire-de-la-formule-deuler-une-rehabilitation-de-la-methode-d
 e-cauchy/
SUMMARY:Jean-Paul Brasselet (I2M\, CNRS\, Marseille): Une démonstration é
 lémentaire de la Formule d'Euler - une réhabilitation de la méthode de 
 Cauchy
DESCRIPTION:Jean-Paul Brasselet: La "formule d'Euler" fait l'objet de multi
 ples controverses : Qui a exprimé le premier cette formule ? Qui en a do
 nné la première (correcte) démonstration ? La démonstration de Cauchy 
 a fait l'objet de critiques sévères\, en particulier de la part de Imre
  Lakatos et de Elon Lima. Dans cet exposé\, après avoir fait un rapide 
 survol de l'historique\, nous donnons une démonstration élémentaire d
 e la formule\, avec pour seul outil la méthode de Cauchy. L'exposé est
  élémentaire et accessible aux étudiants de Maîtrise.\nAvec Nguyen
  Thi Bich Thuy (UNESP\, São José do Rio Preto).\nAn elementary demonstra
 tion of Euler's Formula - a rehabilitation of the Cauchy method \nEuler’
 s formula says that for any sphere triangulation\, the alternate sum: n0
 −n1+n2= 2 where the numbers ni are respectively the number of vertices n
 0\, the number of edges n1 and the number of triangles n2 from the triangu
 lation. There is much controversy about the paternity of the formula\, als
 o about who gave the first correct proof. We provide precisely some elemen
 ts on the history of the formula and also about Cauchy’s first topologic
 al proof. Some authors criticize Cauchy’s proof\, saying the proof needs
  deep topology results that were proven after Cauchy. We show that with a 
 technique of “stretching” and the use of sub-triangulations only\, Cau
 chy’s proof works without using the other results. We use the same tools
  to show that for surfaces such as the torus\, the projective plane and th
 e Klein\, the alternate sum does not depend on the surface. The lecture\, 
 elementary but original\, is a way of rehabilitating Cauchy’s method. Th
 e lecture can be assisted by master students.\nWith Nguyen Thi Bich Thuy (
 UNESP\, São José do Rio Preto).\n\nhttps://arxiv.org/abs/2003.07696\n\n&
 nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Jean-Paul_Brasselet.jpg
CATEGORIES:Groupe de travail,Singularités
LOCATION:St Charles - FRUMAM\, 3\, place Victor Hugo\, Marseille\, 13003\, 
 France
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