[dinga]

Ah yeah and of course at least a bit of Borsuk Ulam. In my own words: "for every continuous function from the n-sphere to R^n, there exists a pair of antipodal points on that sphere that will map to the same point in R^n". Example in 1-D: in a heated a metal-ring with some heat-distribution on it, there are to points exactly opposite from each other which have the same temperature.