Another (fancier!) name for the distance function used in a metric space.

There are a few other uses of the word metric in mathematics, that all revolve around the concept described above:

Met"ric (?), a. [L. metricus, Gr. : cf. F. métrique. See Meter rhythm.]

1.

Relating to measurement; involving, or proceeding by, measurement.

2.

Of or pertaining to the meter as a standard of measurement; of or pertaining to the decimal system of measurement of which a meter is the unit; as, the metric system; a metric measurement.

Metric analysis Chem., analysis by volume; volumetric analysis. -- Metric system, a system of weights and measures originating in France, the use of which is required by law in many countries, and permitted in many others, including the United States and England. The principal unit is the meter (see Meter). From this are formed the are, the liter, the stere, the gram, etc. These units, and others derived from them, are divided decimally, and larger units are formed from multiples by 10, 100, 1,000, and 10,000. The successive multiplies are designated by the prefixes, deca-, hecto-, kilo-, and myria-; successive parts by deci-, centi-, and milli-. The prefixes mega- and micro- are sometimes used to denote a multiple by one million, and the millionth part, respectively. See the words formed with these prefixes in the Vocabulary. For metric tables, see p. 1682. <-- nano-, pico-, femto-, atto-; giga-, tera, etc. -->

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