Jump to navigation Jump to search
|Measures (radius r)|
|Abstract & topological properties|
A circle, also known as a 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[edit | edit source]
The points on a circle are all points such that
where r is the radius of the circle.
Special Properties[edit | edit source]
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.