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Ellipses and Circles (Posted on 2004-11-29) Difficulty: 5 of 5
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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Some Thoughts 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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