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===The interval in a high-dimensional space===
In a [[Euclidean space]], the separation between two points is measured by the distance between the two points. The distance is purely spatial, and is always positive. In spacetime, the separation between two events is measured by the ''invariant interval'' between the two events, which takes into account not only the spatial separation between the events, but also their
:<math>s^2 = \Delta r^2 - c^2\Delta t^2 \,</math>{{spaces|5}}(spacetime interval),
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