Perimeter

see also: Etymology of Perimeter

The perimeter (of the old Greek : perimetros , measurement of the turn) indicates the total Length Contour of a Surface. The perimeter indicates also the Ligne of an unspecified form which closes a surface, it even of an unspecified form.

Perimeter is a synonym the term Circonférence, although the latter rather indicates a closed curved line, near to a Cercle or a ellipse, or length of this curved line.

For all Polygon, the perimeter is worth the nap length of each Côté S of the polygon.

There exist simple Formule S for the basic figures:

Circle

See also: Circumference

$P = 2 \ cdot \ pi \ cdot R$ , where $\ pi$ is the constant pi and R the radius of the circle.
$P = \ pi \ cdot D$ , where D is the Diamètre circle.

These two formulas are perfectly equivalent, since for any circle, $D = 2 \ cdot R$ .

Generalization with the ellipse

$P = \ pi \ cdot (Ra + Rb)$ ,

where $\ pi$ is the constant pi and $Ra$ and $Rb$ the rays or semi-axes of the ellipse.

circular Crown

$P = 2 \ cdot \ pi \ cdot (R + R)$ , where R and R is respectively the radii of small and the large circle of the crown.

Square and Rhombus

$P = 4 \ cdot c$ , where C is the side of the square or the rhombus, according to the case.

Right-angled

$P = 2 \ cdot (L + L)$ , where L and L is respectively the length and the width of the rectangle.

isoperimetric Inequality

See also: Theorem isoperimetric

The perimeter P and the surface have of a noncross polygon check the inequality $P^2 > 4 \ pi A$

See too

Simple: Perimeter Zh-classical: 周界

Random links:

Esclauzels | Cislago | Dag-Otto Lauritzen | Sousa (Paraíba) | Bertrand II of Forcalquier | Coder_la_cage