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Circle
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{{short description|Simple curve of Euclidean geometry}} {{About|the shape and mathematical concept}} {{pp-semi-indef}} {{Use British English|date=September 2016}} {{Use dmy dates|date=February 2023}} {{CS1 config|mode=cs1}} {{Infobox polygon |name = Circle |image = Circle-withsegments.svg |caption = A circle {{legend-line|black solid 3px|circumference ''C''}} {{legend-line|blue solid 2px|diameter ''D''}} {{legend-line|red solid 2px|radius ''R''}} {{legend-line|green solid 2px|centre or origin ''O''}} |symmetry = [[Orthogonal group|{{math|O(2)}}]] |area = {{math|ΟR<sup>2</sup>}} |perimeter = {{math|1=C = 2ΟR}} |type = [[Conic section]] }} A '''circle''' is a [[shape]] consisting of all [[point (geometry)|points]] in a [[plane (mathematics)|plane]] that are at a given distance from a given point, the<!-- This article is written using British English β see WP:ENGVAR, Wikipedia articles should remain with the original variant 'center' is the American English spelling --> [[Centre (geometry)|centre]].<!--see comment before about 'center'--> 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 [[Disk (mathematics)|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 [[gear]]s, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, [[astronomy]] and [[calculus]]. {{TOC limit|3}}<!--To avoid layout breaking when TOC is hidden-->
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