Perim

Perim, short for perimeter, is a measure of the boundary length of a two‑dimensional figure. It represents the distance around the figure and is expressed in units of length, such as meters or feet.

In polygons, the perimeter is the sum of the lengths of all sides. If a polygon has side lengths s1, s2, ..., sn, then P = s1 + s2 + ... + sn. For a circle, the corresponding measure is the circumference, C = 2πr, where r is the radius. Ellipses and other curves do not have a simple closed‑form formula for their perimeters; numerical methods or approximations are typically used.

Key properties include that the perimeter is invariant under translations and rotations of the shape; it scales linearly with the size of the figure. For a fixed area, the circle has the smallest possible perimeter, a statement known as the isoperimetric inequality.

Perimeter is a fundamental concept in geometry and is widely used in surveying, architecture, design, and computer graphics. In mathematical notation, the perimeter is often denoted by P or perim in formulas and software, and is sometimes referred to simply as the boundary length.

Etymology and usage: the term derives from the French périmètre, from Latin and Greek roots meaning around measure. The abbreviation perim is common in technical contexts and in shorthand notes for quick reference to the boundary length of a figure.