All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
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
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information