A220052 Decimal expansion of an ellipsoidal cap height, the cap volume being 1/3 of the ellipsoid volume.

7, 7, 3, 9, 2, 6, 2, 8, 6, 2, 1, 0, 7, 9, 2, 0, 0, 9, 0, 8, 5, 6, 9, 4, 5, 8, 4, 4, 0, 8, 4, 0, 9, 3, 6, 8, 3, 7, 6, 2, 4, 5, 4, 2, 3, 3, 7, 0, 1, 6, 1, 2, 1, 6, 5, 9, 6, 1, 1, 6, 4, 7, 7, 1, 1, 9, 9, 6, 5, 7, 7, 1, 9, 7, 2, 8, 9, 0, 9, 7, 8, 5, 6, 0, 2, 0, 7, 3, 2, 7, 4, 9, 1, 5, 7, 3, 8, 6, 4, 1, 7, 3, 8, 7, 8

Offset

0,1

Comments

Let the equation of the ellipsoid be x^2/a^2 + y^2/b^2 + z^2/c^2 == 1. The volume of the cap cut across the 'a' axis is v(h) = Pi*b*c*(3*a-h)*h^2/(3*a^2). Given v(2a) = 4/3*Pi*a*b*c, and equating v(h) and v(2a)/3, one gets (assuming a=1) the equation 3*h^3 - 9*h^2 + 4 = 0, which is noticeably independant of b or c and valid for a sphere.

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's Mathworld, Ellipsoid

Example

0.773926...

Mathematica

RealDigits[N[Root[3*#^3 - 9*#^2 + 4 & , 2], 105]][[1]]

Crossrefs

Sequence in context: A318386 A318334 A233699 * A153204 A199508 A136478

Adjacent sequences: A220049 A220050 A220051 * A220053 A220054 A220055

Keyword

nonn,cons

Author

Jean-François Alcover, Dec 03 2012

Extensions

Offset changed from 1 to 0 by Bruno Berselli, Jan 03 2013

Status

approved