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Circle

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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

S^1=\Big\{(x,y)\in\R^2:x^2+y^2=1\Big\}

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

D^2=\Big\{(x,y)\in\R^2:x^2+y^2<1\Big\}

as far the closed disk is

\bar{D}^2=\Big\{(x,y)\in\R^2:x^2+y^2\le1\Big\}

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.

Formulas

  • 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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