A circle is a geometric figure which consist of points in the Euclidean plane that are allocated at a fixed distance from the origin. This fixed distance is called the circle's radius.

The precise definition in the Euclidean plane \R^2 is


here the symbol S^1 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: (x-h)^2+(y-k)^2=r^2 (with the origin at (h,k))
  • Circumference of a circle: c=2\pi r=\pi d
  • Area bounded by a circle: \pi r^2 or \frac{cr}{2} .

In all formulas, r is the radius, d is the diameter, and c is the circumference.

See also

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