Perimeter

A perimeter is a path that surrounds a two-dimensional shape. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length—it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference.

Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.

The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with ${\displaystyle \int _{0}^{L}\mathrm {d} s}$, where ${\displaystyle L}$ is the length of the path and ${\displaystyle ds}$ is an infinitesimal line element. Both of these must be replaced with by algebraic forms in order to be practically calculated. A generalized notion of perimeter, which includes hypersurfaces bounding volumes in ${\displaystyle n}$-dimensional Euclidean spaces, is described by the theory of Caccioppoli sets.

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