A New Proof of Cavalieri's Quadrature Formula

In 1635, Bonaventura Cavalieri (1598-1647) published his "Geometria indivisibilibus," in which he outlined a method to compute areas and volumes by subdividing regions into infinite numbers of infinitesimal slices and suitably rearranging. Wildberger interprets later mathematicians' p...

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Veröffentlicht in:	The American mathematical monthly 2002-11, Vol.109 (9), p.843-845
1. Verfasser:	Wildberger, N. J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Approximations and expansions Calculus Exact sciences and technology Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Sciences and techniques of general use
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Zusammenfassung:	In 1635, Bonaventura Cavalieri (1598-1647) published his "Geometria indivisibilibus," in which he outlined a method to compute areas and volumes by subdividing regions into infinite numbers of infinitesimal slices and suitably rearranging. Wildberger interprets later mathematicians' proofs of this as utilizing a formula to evaluate a Riemann sum. Wildberger offers a proof of Cavalieri's formula that uses the (hidden) symmetry of the function "xn" and the Binomial Theorem, sidestepping the use of Riemann sums altogether.
ISSN:	0002-9890 1930-0972
DOI:	10.1080/00029890.2002.11919920