
 Fractal Dimension 
  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. 
  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. 
  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) 
