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Home > Art, Film & Photography > Fraction: Nombre Rationnel, Fraction Continue, Developpement Decimal Periodique, Fraction Egyptienne, Suite de Farey, Theoreme D
Fraction: Nombre Rationnel, Fraction Continue, Developpement Decimal Periodique, Fraction Egyptienne, Suite de Farey, Theoreme D

Fraction: Nombre Rationnel, Fraction Continue, Developpement Decimal Periodique, Fraction Egyptienne, Suite de Farey, Theoreme D


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About the Book

Ce contenu est une compilation d'articles de l'encyclopedie libre Wikipedia. Pages: 28. Non illustre. Chapitres: Nombre rationnel, Fraction continue, Developpement decimal periodique, Fraction egyptienne, Suite de Farey, Theoreme de Midy, Fraction unitaire, Fraction dyadique, Cercle de Ford, Fraction irreductible, Theoreme de Wolstenholme, Denominateur, Un demi, Conjecture d'Erd s-Straus, Numerateur. Extrait: En mathematiques, une fraction continue ou fraction continue simple ou encore fraction continuee est une expression de la forme: .comportant un nombre fini ou infini d'etages. Une fraction continue generalisee est l'analogue d'une fraction continue, mais avec les 1 remplaces par des valeurs bj: .Le present article porte principalement sur les fractions continues simples. On montre qu'on peut representer tout nombre reel sous forme d'une fraction continue, finie ou infinie, dans laquelle a0 est un entier relatif et les aj sont des entiers strictement positifs. Le sens du mot representer sera precise ulterieurement. Comme dans la notation decimale usuelle, ou chaque nombre reel est approche par des nombres decimaux de plus en plus precisement au fur et a mesure de la donnee des decimales successives, de meme chaque nombre reel est approche par des fractions etagees de la forme ci-dessus de plus en plus precisement au fur et a mesure qu'on rajoute des etages. En outre, s'il faut une infinite de decimales pour decrire exactement un nombre non decimal, il faut un developpement infini en fraction continue pour decrire exactement un nombre irrationnel. Les fractions continues sont utiles en approximation diophantienne, notamment parce qu'elles fournissent, en un certain sens, les meilleures approximations des nombres reels par des nombres rationnels. Cette propriete est a l'origine d'algorithmes pour l'approximation de racines carrees, mais aussi de demonstrations d'irrationalite voire...



Product Details
  • ISBN-13: 9781159474126
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 92
  • Spine Width: 2 mm
  • Weight: 73 gr
  • ISBN-10: 1159474125
  • Publisher Date: 01 Oct 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Nombre Rationnel, Fraction Continue, Developpement Decimal Periodique, Fraction Egyptienne, Suite de Farey, Theoreme D
  • Width: 189 mm


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