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 Ellipses and Circles (Posted on 2004-11-29)
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.

 No Solution Yet Submitted by Brian Smith Rating: 4.0000 (4 votes)

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 Initial thoughts... | Comment 1 of 6

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

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