perimet

Perimet is the boundary length of a closed planar figure, representing the total distance around the outside. In English this quantity is called the perimeter; in many languages a cognate form such as "perimet" is used, and the term appears in various mathematical and technical contexts. The perimet is a one-dimensional measure of the exterior boundary.

For polygons, the perimet is the sum of the lengths of its sides. For smooth curves, it is the arc length of the boundary. If the boundary is described by a parametric curve r(t) with t in [a,b], the perimet equals the integral of the speed, ∫_a^b |r'(t)| dt. Special cases: a rectangle with sides a and b has perimet 2(a+b); a circle with radius r has perimet 2πr.

Properties include invariance under translations and rotations. The perimet scales linearly with uniform scaling: if the figure is scaled by a factor s, the perimet multiplies by s. For the union of disjoint figures, the perimet is the sum of their perimeters; for shapes sharing edges, the external boundary depends on the shared boundary and may be smaller than the sum of individual perimeters.

Applications of the perimet span many fields. It is used in architecture, land surveying, robotics, computer graphics, and geographic information systems to quantify boundary length, inform material estimates, plan paths, or assess boundary-related constraints.

Origin and terminology trace the concept to the Greek roots peri, around, and metron, measure, passing into modern languages as a cognate form related to perimeter. See also perimeter.