# Circle (mathematics)

A **circle** is a curve, consisting of those points in a plane that are a given distance away from a single point, the centre. The term may also refer to similarly defined curves on other two-dimensional manifolds.

The circle has been of incredible interest to mathematicians since mathematics' foundation. The circle serves as the starting point for much of mathematics, for example **π** was first encountered as the ratio of a circle's diameter to its circumference.

*x*-coordinate is given by , the

*y*-coordinate is given by and the gradient of the radius from the centre (0,0) to the point (

*x*,

*y*) is given by where is the angle between the radius and the

*x*-axis.

The circle is also one of the 4 conic sections. It is represented algebraically as where the circle's centre is the point (*a*,*b*) and it has radius *r*.

In the complex plane a circle is represented by the locus that satisfies the equation ; in this case the circle would have centre *a* and radius *r*.

A given circle of radius *r* has circumference 2π*r* and area π*r*^{2}.