In a square of side 4, I pack 4 circles of unit radius.

What's the largest circle I can fit into the center (such that it doesn't overlap the other circles)?

Well, Richard, you can do this this with just one of the blue circles, too. Take the upper left one and set a 1x1 square around it. The diagonal (upper left corner to lower right corner) is clearly squareroot of 2. Subtract the unit 1 circle leaving the quarter red circle with its radius plus the same distance as that radius in the opposite corner. So, the radius = ((sqrt2)-1)/2.

Hugs. CeeAnne

Ps - And the reason I edited my Comment 8 subject titled Please Note was because the squareroot sign was corrupted.

Posted by CeeAnne on 2004-10-20 02:30:00