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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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Dec 03 2012

EXTENSIONS

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

STATUS

approved

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Last modified August 11 19:26 EDT 2022. Contains 356066 sequences. (Running on oeis4.)