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.