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
Coordinates for the points of a unit circle are given by all points (x, y) such that


 * x2 + y2 = 1.

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.