A "perimeter" is a path that surrounds a two-dimensional shape. The word comes from the Greek "peri" and "meter" . 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 considerable practical applications. The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel 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 \int_0^L \mathrm s where L is the length of the path and ds is an infinitesimal line element. Both of these must be replaced with other algebraic forms in order to be solved: an advanced notion of perimeter, which includes hypersurfaces bounding volumes in n -dimensional Euclidean spaces can be found in the theory of Caccioppoli sets.
Polygons are fundamental to determining perimeters, not only because they are the simplest shapes but also because the perimeters of many shapes are calculated by approximating them with sequences of polygons tending to these shapes. The first mathematician known to have used this kind of reasoning is Archimedes, who approximated the perimeter of a circle by surrounding it with regular polygons.
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