Right, if surface means the d-dimensional sphere S^d. ((( A famous problem was how many differently colored hairs can be orthogonal at each point of S^d, if each color of hair is continuous and of positive length over all of S^d. The curious answer (1962) is that if 2^k is the largest power of 2 dividing d+1, then the maximum number of colors is max(d) = 2^(k mod 4) + 8*floor(k/4) - 1. ))) --Dan << --yah, but really, we want d different color hairs, and the green hairs are combed, the red hairs are combed in a direction always orthogonal to the green hairs etc. For that more powerful kind of combing, you can do it for a surface that is 1,3, or 7 dimensional using complex, quaternion, octonion tricks in the d+1 dimensional space...
________________________________________________________________________________________ It goes without saying that .