On the surface area of the ellipsoid
Author: Stuart R. Keller
Journal: Math. Comp. 33 (1979), 310-314
MSC: Primary 65D30; Secondary 53A05
MathSciNet review: 514826
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Abstract: An expression is derived for the surface area of an ellipsoid in the form of a convergent series. The derivation is based upon an n-point Gauss-Chebyshev numerical quadrature. The rate of convergence and accuracy of the formula are demonstrated by computing the surface area of several ellipsoids.
P. J. DAVIS & P. RABINOWITZ, Numerical Integration, Blaisdell, Waltham, Mass., 1967. MR 35 #2482.
Standard Mathematical Tables, 14th ed. (S. M. Selby, Editor), The Chemical Rubber Co., Cleveland, Ohio, 1965.