### metric

(mathematical generalization of the concept of distance)

A **metric** is a generalization of distance, capturing
some of the characteristics of distance. It is a function
of pairs of points in a *space* to a non-negative number,
such that the metric from a point to itself is zero,
that applying it to the reverse (i.e., B to A instead
of A to B) yields the same result, and that the metric
from A to C is always less than or equal to the metric
from A to B plus that of B to C, all statements that
would hold true of ordinary distance.

In physics, metrics of non-straight lines are of
interest, e.g., specifying "the metric of A to C through B",
and for curved lines in continuous spaces, using a line integral.

A variation on the *metric* concept is relevant to
space-time in relativity, i.e., a metric,
but allowing a zero metric in some cases where points are distinct.
Examples are the **Minkowski metric** used for special relativity
(relativistically invariant, i.e.,
invariant under the Lorentz transformation),
the **Schwarzschild metric** for general relativity given the
influence of a mass, and the **Robertson-Walker metric**
incorporating GR and the expansion/contraction of
a model universe.

(*mathematics,physics,relativity*)
http://en.wikipedia.org/wiki/Metric

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