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Educación matemática

versión impresa ISSN 1665-5826

Resumen

PRABHU, Vrunda  y  CZARNOCHA, Bronislaw. Los indivisibles en el cálculo contemporáneo. Educ. mat [online]. 2008, vol.20, n.1, pp. 53-88. ISSN 1665-5826.

Arithmetica Infinitorium of John Wallis is the arithmetization of the work Geometria Indivisibilibus of Bonaventura Cavalieri, both of which utilised the indivisible. The Method of Archimedes found only in 1910 also utilised the indivisible. These works predate the current ubiquitious use of the concept of the limit. The formulations presented in this article reformulate the work of Wallis and Cavalieri providing contemporary rigorous mathematical foundations, viz., the limit concept Two integrals, Cavalieri-Wallis and Porter-Wallis integrals, are formulated on the basis of student intuition, and the Indivisible of Archimedes, Cavalieri and Wallis. These integrals provide a new viewpoint on classical concepts of measure, area and the definite integral. Cavalieri-Wallis construction clarifies ambiguities of Cavalieri Principle, replacing "all the lines" in the work of Archimedes and Cavalieri. The visually appealing Porter-Wallis construction anchors the concept of area in a statistical framework, which informs the traditionally difficult pedagogy of the Riemann integral in freshman Calculus teaching experiments conducted at various sites in the United States and Mexico.

Palabras llave : indivisible; definite integral; Riemann integral; Porter-Wallis integral; Cavalieri-Wallis integral.

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