Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-03T12:29:31.220Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximations to the Area of ann-Dimensional Ellipsoid

Published online by Cambridge University Press:  20 November 2018

D. H. Lehmer
D. H. Lehmer*
Affiliation:
University of California
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The fact that the perimeter S(a, b) of an ellipse is not an elementary function of its semiaxes a, b has led to many suggested approximations of S in finite form.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 267 - 282
Copyright
Copyright © Canadian Mathematical Society 1950

References

[1] Johann Kepler, , Opera Omnia, vol. 3 (1609), 401–402.Google Scholar
[2] Barbarin, P., Note sur le périmèter de l'ellipse, Mathesis, s. 1, vol. 2 (1882), 209.Google Scholar
[3] Mansion, P., Sur le perimèter de l'ellipse, Mathesis, s. 1, vol. 2 (1882), 211–216.Google Scholar
[4] Muir, T., On the perimeter of an ellipse, Messenger Math., vol. 12 (1883), 149.Google Scholar
[5] Boussinesq, J., Cours d'analyse infinitesimale (Paris, 1890), vol. 2, 74–77.Google Scholar
[6] Peano, G., Valori approssimati per l'area di un ellissoide, Rome, R. Accad. dei Lincei, Rendiconti, vol. 6: 2 (1890), 317–321.Google Scholar
[7] Pόlya, G., Approximations to the area of the ellipsoid , Publicaciones del Institute de Matematica, Rosario, vol. 5 (1943), 13 pp.Google Scholar
[8] Pόlya, G. and Szegö, G. , Inequalities for the capacity of a condenser, Amer. J. Math., vol. 67(1945), 1–32.Google Scholar