The precise definition in the Euclidean plane is
here the symbol is the modern name used in the math-science. In contrast an open disk -in the euclidean plane- is defined as
as far the closed disk is
Observe that the circle is the frontier of both, not included in the open one but included in the closed.
In informal discussion people tend to confuse a circle with a disk.
- General equation for a circle: (with the origin at )
- Circumference of a circle:
- Area bounded by a circle: or .