Perimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

A calculated perimeter is the length of fence required to surround a yard or garden.

can be computed as follows: A generalized notion of perimeter, which includes hypersurfaces bounding volumes in

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.

[1] The perimeter of a polygon equals the sum of the lengths of its sides (edges).

A regular polygon may be characterized by the number of its sides and by its circumradius, that is to say, the constant distance between its centre and each of its vertices.

If R is a regular polygon's radius and n is the number of its sides, then its perimeter is A splitter of a triangle is a cevian (a segment from a vertex to the opposite side) that divides the perimeter into two equal lengths, this common length being called the semiperimeter of the triangle.

The perimeter of a circle, often called the circumference, is proportional to its diameter and its radius.

Indeed, a commonplace observation is that an enlargement (or a reduction) of a shape make its area grow (or decrease) as well as its perimeter.

Proclus (5th century) reported that Greek peasants "fairly" parted fields relying on their perimeters.

The convex hull of a figure may be visualized as the shape formed by a rubber band stretched around it.

[3] In the animated picture on the left, all the figures have the same convex hull; the big, first hexagon.

The isoperimetric problem is to determine a figure with the largest area, amongst those having a given perimeter.

In particular, to find the quadrilateral, or the triangle, or another particular figure, with the largest area amongst those with the same shape having a given perimeter.

The word comes from the Greek περίμετρος perimetros, from περί peri "around" and μέτρον metron "measure".