Circle

A circle, or 1-sphere is the set of all points on a 2D plane that are a certain distance away from a given point. This distance is known as the radius. Circles are one of the fundamental figures in geometry, and is instrumental in constructing more complex polygons through the use of straightedge and compass construction. A circle is also the limit of a n-gon as n approaches infinity. However, a circle itself is not considered to be a polygon.

A circle is also a special case of an ellipse, where the eccentricity is equal to 0.

Vertex Coordinates
If a circle is considered to be made of up infinitely many edges, then the vertices of a circle are every point [x,y] such that

x2 + y2 = r2

where r is the radius of the circle.

Special Properties
Circles have many unique properties among the 2D shapes. These include:


 * They are rotationally symmetric from every angle.
 * They have the lowest perimeter-to-area ratio of any closed 2D shape.
 * They have a constant width.