# Geometry problem

Joe Felsenstein joe at evolution.genetics.washington.edu
Thu Oct 9 14:31:38 EST 1997

In article <61cjm4\$dr0 at rzunews.unizh.ch>,
Dr. S. Shapiro <toukie at zui.unizh.ch> wrote:
>     Eccentricity e of spheroid = [1 - (b^2/a^2)]^(1/2)
>
>     then given a numerical value for the volume of a sphere, is there a
>unique value for the eccentricity of a spheroid with the same volume?
>
>     For example, I have two spheres, one with a volume of 357 cm^3 and
>the other with a volume of 372 cm^3.  What would be the eccentricities
>of spheroids with volumes of 357 cm^3 and 372 cm^3?

Stated that way, the answer is:  zero.

The two spheres *are* spheroids, so one can achieve the same volume as each,
By having two spheres (of eccentricity zero), one of volume 357 cm^3 and the
other of volume 372 cm^3 (they are identical to themselves).

But I suspect Shapiro intended to post some other, more substantive, problem.

--
Joe Felsenstein         joe at genetics.washington.edu
Dept. of Genetics, Univ. of Washington, Box 357360, Seattle, WA 98195-7360 USA