Geometry/Perimeter and Arclength

Perimeter of CircleEdit

The circles perimeter   can be calculated using the following formula


where   the radius of the circle.

Perimeter of PolygonsEdit

The perimeter of a polygon   with   number of sides abbreviated   can be caculated using the following formula


Arclength of CirclesEdit

The arclength   of a given circle with radius   can be calculated using


where   is the angle given in radians.

Arclength of CurvesEdit

If a curve   in   has the parametric form   for   , then the arclength can be calculated using the following fomula


Derivation of formula can be found using differential geometry on infinitely small triangles.