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Article ID: CBB000932308

Le problème de la définition de l'aire d'une surface gauche: Peano et Lebesgue (2009)

Gandon, Sébastien (Author)
Perrin, Yvette (Author)

Archive for History of Exact Sciences
Volume: 63
Pages: 665--704

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At the beginning of the 1890s, Schwarz and Peano (independently of each other) showed that Serret's definition of the area of a surface was flawed. This paper first aims at describing the various methods that the mathematicians have used for correcting Serret's reasoning; its second goal is to compare and to present more in detail two solutions: Lebesgue's notorious construction and Peano's definition.

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