This article is about the shape and mathematical concept. For other uses, see Circle (disambiguation).
Circle
A circle
circumference C
diameter D
radius R
centre or origin O
Type Conic section
Symmetry group O(2)
Area πR2
Perimeter C = 2πR
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc.
The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus.
Terminology
Annulus: a ring-shaped object, the region bounded by two concentric circles.
Arc: any connected part of a circle. Specifying two end points of an arc and a centre allows for two arcs that together make up a full circle.
Centre: the point equidistant from all points on the circle.
Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments.
Circumference: the length of one circuit along the circle, or the distance around the circle.
Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; or the length of such a line segment. This is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord for a given circle, and its length is twice the length of a radius.
Disc: the region of the plane bounded by a circle. In strict mathematical usage, a circle is only the boundary of the disc (or disk), while in everyday use the term "circle" may also refer to a disc.
Lens: the region common to (the intersection of) two overlapping discs.
Radius: a line segment joining the centre of a circle with any single point on the circle itself; or the length of such a segment, which is half (the length of) a diameter. Usually, the radius is denoted
𝑟
{\displaystyle r} and required to be a positive number. A circle with
𝑟
=
0
{\displaystyle r=0} is a degenerate case consisting of a single point.
Sector: a region bounded by two radii of equal