1. Find the ellipse of smallest area which circumscribes 2 non-overlapping unit circles.
2. Find the ellipse of smallest area which circumscribes 3 non-overlapping unit circles.
The area of an elipse is defined as pi*x*y.
The circumfrance of the elipse can be drawn by:
X = a*cos(c)
Y = b*sin(c)
Where c = 0 -> 2*pi and a and b are multipliers used to warp the elipse away from a perfect circle. when a and b are both 1, you get a circle with radius 1.
For the two circle condition, the smallest area would have the circles in a line (obviously) and touching (also obviously).
For the three circle condition, I think that one circle (the middle one) would be slightly out of line from the other two. Probably not to the extent that their centers form a regular triangle, more likely an obtuse triangle. I think an angle of 120° would be a good place to start.
This is definitely a problem best solved programatically.
Posted by Erik O.
on 2004-11-29 19:02:37