OK I have a computer game and I need a method of programming in for any given map, proof that I have cirumnavigated the globe let's say the range is in co-ordinates 0,0 to 300,300 or 90,000 squares. How can I prove that Unit 1 or U1 has passed from say point a at (grenwich mean) GM or whatever arbitrary start line of longitude say a1 and back to a point at the line of longitude a1? This isn't a homework question it refers to a particular computer game. I guess what I'm asking is can you program a mathematical expression which will give a 1 or 0 answer to has the ship circumnavigated the globe/map, assume you cant cross the poles and any method requires going round continents and land masses? Is this possible or not? Assume the data set for using the equation is every point that the ship passes through either in a diferential form dx/dy= derived from the data set as a whole, or as a set of all the points of the ships passage either is fine. If I apply the equation with logical espressions consistent with say C++ or some sort of maths language, to the data set would I get a 0 or 1 answer using logical expressions or is this just not possible?