Geometry/Perimeter and Arclength

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Perimeter of Circle[edit]

The circles perimeter can be calculated using the following formula

where and the radius of the circle.

Perimeter of Polygons[edit]

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

.

Arclength of Circles[edit]

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

where is the angle given in radians.

Arclength of Curves[edit]

If a curve in have a parameter 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.