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)?
A square formed by the center of one of the large blue circles, the points of tangency of this circle with its neighboring circles, and the center of the small red circle, is 1 unit on a side and has as its diagonal the sum of the radii of the large and small circles. The diagonal is √2, so the radius of the center circle is (√2) - 1.
Posted by Charlie
on 2004-01-13 09:27:05