1. bookVolume 29 (2021): Edizione 2 (June 2021)
Dettagli della rivista
License
Formato
Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
Lingue
Inglese
access type Accesso libero

A Generalization of Archimedes’ Theorem on the Area of a Parabolic Segment

Pubblicato online: 08 Jul 2021
Volume & Edizione: Volume 29 (2021) - Edizione 2 (June 2021)
Pagine: 199 - 209
Ricevuto: 24 Sep 2020
Accettato: 15 Nov 2020
Dettagli della rivista
License
Formato
Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
Lingue
Inglese
Abstract

Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1).

Keywords

MSC 2010

[1] L. E. Blumenson, A derivation of n-Dimensional Spherical Coordinates, The American Mathematical Monthly, Vol. 67, No. 1 (1960), pp. 63-66. Search in Google Scholar

[2] T. Dance, G. Swain, Archimedes’ Quadrature of Parabola Revisited, Mathematics Magazine, Vol. 71, No. 2 (1998), pp. 123-130. Search in Google Scholar

[3] T. L. Heath, The Works of Archimedes, C. J. Clay and Sons, London, 1897. Search in Google Scholar

[4] W. Rudin, Principles of the Mathematical Analysis, third edition, McGraw-Hill, Inc., New York, 1976. Search in Google Scholar

Articoli consigliati da Trend MD

Pianifica la tua conferenza remota con Sciendo