

A220052


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


0



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
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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*ah)*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

JeanFrançois Alcover, Dec 03 2012


EXTENSIONS

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


STATUS

approved



