
 Fractal Dimension 
  The dimension of the union of finitely many sets is the largest dimension of any one of them, so if we ``grow hair'' on a plane, the result is still a twodimensional set. 
  Not surprisingly, the box dimensions of ordinary Euclidean objects such as points, curves, surfaces, and solids coincide with their topological dimensions of 0, 1, 2, and 3 this is, of course, what we would want to happen, and follows from the discussion at the beginning of §5.1. 
  Thus, the embedding dimension of a plane is 2, the embedding dimension of a sphere is 3, and the embedding dimension of a klein bottle is 4, even though they all have (topological) dimension two. 
 www.math.sunysb.edu /~scott/Book331/Fractal_Dimension.html (1303 words) 
