now here you siafu go misquoting me again i did not describe the solution of the navigation equations as the intersection of three spheres i said i clearly understand that the gps navigation equations consist of n n greater than equations for the surfaces of n spheres and that the solution of these n equations consists of a clock bias and a point at the intersection of these n sphere surfaces this of course implies that the position part of the solution is at an intersection of any three of the n spheres but this is not a description of the solution but instead an implication of the solution kendall credentials certainly do matter since if you don't have the proper education then you can't understand the material and are certainly unqualified to write also kendall pride is a virtue i am very proud that i have received a superior quality of education and that i have had a highly successful engineering career the fact that i have the great virtue of pride does not mean that i do not treat others with respect and civility dvdm you start your post with the word that's this usage of the word that is very vague and ambiguous in this context also you need to say what you are talking about rather than make some reference