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 called the radius. Circles are not considered to be polygons, as they cannot be meaningfully assigned any elements other than points.

A circle is the 1-dimensional hypersphere.

Formally, a filled-in circle is called a disk, and its boundary is called a circle. A disk is the 2-dimensional hyperball.

Coordinates
The points on a circle are all points (x,y) such that


 * $$x^2+y^2=r^2$$

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.
 * Their center of mass's cycloid is a straight line.