login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 20:25 EST 2019. Contains 329848 sequences. (Running on oeis4.)