métrique

Métrique is a French term used in several related domains to denote measurement, structure, or distance. Its exact meaning depends on the context, encompassing mathematics, poetry, and systems of measurement.

In mathematics, métrique corresponds to the notion of a metric. A metric is a function d on a set X that assigns a nonnegative real number to each pair of elements and satisfies four conditions: positivity, identity of indiscernibles (d(x,y)=0 iff x=y), symmetry (d(x,y)=d(y,x)), and the triangle inequality (d(x,z) ≤ d(x,y)+d(y,z)). A set equipped with a metric is called a metric space and supports a notion of distance, which in turn induces a topology, notions of convergence, and continuity. Common examples include the Euclidean metric, the Manhattan (l1) metric, and the discrete metric. The concept also admits variants such as pseudometrics, quasi-metrics, and ultrametrics.

In the field of literature, métrique concerns the study of verse rhythm and structure, i.e., prosody. It analyzes patterns of syllables and accents to determine the meter of a line or stanza. In French poetry, traditional forms such as the alexandrine (twelve syllables) exemplify métrique, as do other syllable-based lengths like decasyllables or octosyllables. Métrique also considers phenomena that affect rhythm, including elision, enjambment, and masculine or feminine endings.

Historically, métrique can also refer to the metric system or decimal system of measurement (système métrique), established during the French Revolution and now part of the International System of Units (SI). In that sense, it denotes a framework for units such as the metre, the kilogram, and the litre used worldwide.