1. Find the ellipse of smallest area which circumscribes 2 nonoverlapping unit circles.
2. Find the ellipse of smallest area which circumscribes 3 nonoverlapping unit circles.
(In reply to
As far as I plan to get by Jer)
I didn't realize until I read Erik O.'s post that I actually solved part 1 and that part 2 is much easier.
If you want the ABSOLUTE minimum for ANY circles, make then touching (duh). This makes d=1 in my previous post. The expression to minimize (from [7]) is
b*sqrt(b^4/(b^2  1)
I still woudn't take the derivative but the approximate solution is a=2.1213, b=1.2247, area = 8.162
Part 2 is even easier as the minimal ellipse is a circle of radius 1+2(3)/3 = 2.1547 which has area 14.5856
Jer

Posted by Jer
on 20041129 19:30:44 