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Article ID: CBB000933314

Euler Transgressing Limits: The Infinite and Music Theory (2008)

Quaderns d'Història de l'Enginyeria
Volume: 9
Pages: 9--24

ISSN: 1135-934X

URI: http://hdl.handle.net/2099/8052

Publication Date: 2008
Edition Details: Part of a special issue: 300 Aniversari de Leonhard Euler (1707--2007)
Language: English

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Infinity Music theory Sequences and series (mathematics) Mathematics 18th century Euler, Leonhard

Leonhard Euler was one of the most creative mathematicians of all time. One of the characteristics of his creativity is his transgression or removal of limits. Four examples are discussed in order to illustrate this assertion. 1. Mathematical rigour: Euler claimed to have restored mathematical rigour in the analysis of the infinite. 2. Zeta-function for s = 2: Euler found the value of the series of the reciprocal square numbers by treating it as an algebraic equation of infinite degree. 3. Divergent series: He introduced a new notion of sum in order to avoid the use of divergent series. 4. Music theory: He abolished the distinction between consonances and dissonances.

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Article Massa Esteve, Maria Rosa (2008) Congrés Internacional “300 Aniversari Leonhard Euler (1707--2007)”. Barcelona, 20--21 de setembre de 2007. Quaderns d'Història de l'Enginyeria (p. 307). unapi

Article Lusa Monforte, Guillermo (2008) Congrés Internacional “300 Aniversari Leonhard Euler (1707--2007)”. Una presentación informal. Quaderns d'Història de l'Enginyeria (p. 3). unapi

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