Fall 2003 

The number of squares of length 1/n needed to cover the circle grows linearly with n. The circle has dimension 1.  The number of squares of length 1/n needed to cover the dis grows like n^{2}. The disk has dimension 2. 
On the other hand, the number of squares of length 1/n needed to cover the coast of Massachusetts grows like n^{d} with a number d between 1 and 2. The curve appears to be a fractal. The measurement of the number of squares is a counting exercice. The computation of the growth rate needs a linear fit. ( More Details (PDF)) 