The circles perimeter
can be calculated using the following formula
![{\displaystyle O=2\pi r}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7864e409aa4e687d49ea78de0ba36064acac3498)
where
the radius of the circle.
The perimeter of a polygon
with
number of sides abbreviated
can be calculated using the following formula
.
The arclength
of a given circle with radius
can be calculated using
![{\displaystyle b={\frac {v}{2\pi }}2\pi r=vr}](https://wikimedia.org/api/rest_v1/media/math/render/svg/791a0e5188ddc67290813e44c118ffc50544558f)
where
is the angle given in radians.
If a curve
in
has the parametric form
for
, then the arclength can be calculated using the following fomula
![{\displaystyle S=\int \limits _{a}^{b}{\sqrt {\left({\frac {dx}{dt}}\right)^{2}+\left({\frac {dy}{dt}}\right)^{2}+\left({\frac {dz}{dt}}\right)^{2}}}\,dt=\int _{\gamma }{\sqrt {\left({\frac {dx}{dt}}\right)^{2}+\left({\frac {dy}{dt}}\right)^{2}+\left({\frac {dz}{dt}}\right)^{2}}}\,dt}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f05a18ca15af7b600aa81d221af986efb8ee7d59)
Derivation of formula can be found using differential geometry on infinitely small triangles.