We investigate the use of non-homogeneous spherical poly-nomials for the approximation of functions deened on the sphere S 2. A spherical polynomial is the restriction to S 2 of a polynomial in the three coordinates x; y; z of R 3. Let P d be the space of spherical polynomials with degree d. We show that P d is the direct sum of H d and H d?1 , where H d denotes the space of homogeneous degree-...

We consider a formalization of the following problem. A salesperson must sell some quota of brushes in order to win a trip to Hawaii. This salesperson has a map (a weighted graph) in which each city has an attached demand specifying the number of brushes that can be sold in that city. What is the best route to take to sell the quota while traveling the least distance possible? Notice that unlik...