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- W2497392249 abstract "Publisher SummaryThis chapter focuses on distance preserving transformations. Geometrical notions of distance are often many and varied and some conservatively remain close to the canonical Euclidean distance, with its triangle inequality, additivity along lines. Distances need no longer be positive, symmetry disappears, and about all that remains is a space with scalars somehow assigned to pairs of its points. Alexandrov's theorem concerns distance preserving transformations of Minkowski space-time, the geometrical space of special relativity theory. Minkowski space-time is an amalgam of ordinary three-dimensional Euclidean space with time; specifically, if Euclidean space is coordinatized as usual by rectangular coordinates (x, y, z) Є R3 and time t Є R is measured by some clock, then the events of Minkowski space-time are described by coordinates (t,x,y,z) Є R4. Structure for the set of events comes from the basic axiom of relativity theory: unreflected light signals travel in straight lines with the same speed in all directions." @default.
- W2497392249 created "2016-08-23" @default.
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- W2497392249 date "1995-01-01" @default.
- W2497392249 modified "2023-09-25" @default.
- W2497392249 title "Distance Preserving Transformations" @default.
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- W2497392249 doi "https://doi.org/10.1016/b978-044488355-1/50018-9" @default.
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