Blending two major techniques in order to compute π

Resultado de la investigación: Contribución a una revistaArtículo

Resumen

Three major techniques are employed to calculate π. Namely, (i) the perimeter of polygons inscribed or circumscribed in a circle, (ii) calculus based methods using integral representations of inverse trigonometric functions, and (iii) modular identities derived from the transformation theory of elliptic integrals. This note presents a combination of the first two procedures, which allows the derivation of a family of series that may exhibit very fast convergence rates. The geometrical interpretation gives good insight into the acceleration method that is being implemented.

Idioma originalInglés
Páginas (desde-hasta)85-92
Número de páginas8
PublicaciónInternational Journal of Mathematical Education in Science and Technology
Volumen36
N.º1
DOI
EstadoPublicada - 1 ene 2005

Huella dactilar

Inverse trigonometric function
Elliptic integral
Perimeter
Integral Representation
Polygon
Convergence Rate
Calculus
Circle
Calculate
Series
Family
Interpretation

Citar esto

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Blending two major techniques in order to compute π. / Fernandez Guasti, Manuel.

En: International Journal of Mathematical Education in Science and Technology, Vol. 36, N.º 1, 01.01.2005, p. 85-92.

Resultado de la investigación: Contribución a una revistaArtículo

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