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 independent of b or c and valid for a sphere.
LINKS
Eric Weisstein's Mathworld, Ellipsoid
EXAMPLE
0.77392628621079200908569458440840936837624542337...
MATHEMATICA
RealDigits[N[Root[3*#^3 - 9*#^2 + 4 & , 2], 105]][[1]]
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Dec 03 2012
EXTENSIONS
Offset changed from 1 to 0 by Bruno Berselli, Jan 03 2013
STATUS
approved