There are two balls each having the precise shape of an Oblate Spheroid, and each having the equatorial radius and the polar radius respectively as 125 cm and 80 cm, lying on a perfectly horizontal floor on their respective polar axes and touching each other.

What is the diameter of the largest spherical ball that can pass through the gap between the oblate spheroids and the floor?

This is harder than I thought it would be.  Basically we just need a circle between two ellipses and the floor.  I figured the resulting equation would be a quadratic whose discriminant needs to be zero. 

Unfortunately it is a rather unpleasant looking quartic.  The approximate solution is about r=23.47

Posted by Jer on 2014-07-07 00:28:57