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... A space where distance
is given with no minus signs is called "Euclidean". There are many
useful multi-dimensional Euclidean spaces. The most notable are
the phase-spaces for many particles. A "phase-space" is a space where
the coordinates are the respective positions (3 coordinates each) and
momenta (3 coordinates each) of each particle. Phase space for 3 particles
is 18-dimensional. ...