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A circle is a form made up of all points on a plane that are at the same distance from a central point. It’s the curve drawn out by a point moving in a plane while keeping its distance from a particular point constant. The radius is the distance between any point on the circle and the center. In most cases, the radius must be a positive integer. A degenerate instance is a circle with displaystyle r=0r=0. Except when otherwise specified, this article is about circles in Euclidean geometry, specifically the Euclidean plane.

A circle, in particular, is a closed curve that splits the plane into two regions: inner and exterior. In ordinary usage, the phrase “circle” can refer to either the figure’s boundary or the entire figure, including its inside; in precise technical terms, the circle is merely the boundary, and the entire figure is referred to as a disc.

A circle can alternatively be described as a specific type of ellipse in which the two foci are coincident, the eccentricity is zero, and the semi-major and semi-minor axes are equal; or the two-dimensional form encompassing the maximum area per unit perimeter squared, as determined by calculus of variations.

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