This suggest an interesting, though difficult, contour plot to make in the 1st quadrant of the plane: F(x,y) = the largest number of diameter-1 circles that can be packed in an x*y rectangle. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of Erich Friedman Sent: Wed 5/18/2005 11:38 AM To: math-fun Subject: Re: [math-fun] Packing circles into a finite rectangle

If you have circles of radii 1/1, 1/2, 1/3, ..., 1/n for all n >= 1, then their total area is finite, although the sum of their radii is infinite.

Can one fit these circles into a finite-sized rectangle?

yes, they will fit inside a 1 x (11/6) rectangle for example. put each circle inside a square, and then pack the squares like this: http://www.stetson.edu/~efriedma/harmonic/ erich _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun