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RE: Multiple dimensions...



Jack U. writes:
... 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. ...

Actually, the geometry of phase space is symplectic, not Euclidean.

David Bowman
Georgetown College
dbowman@gtc.georgetown.ky.us