circle

Also known as round shape, 1-sphere, circle line, non-filled circle

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.

AI overview

A circle is a perfectly round shape made up of all points that sit at the same distance from a central point, called the radius. Circles are fundamental geometric shapes that appear throughout mathematics, nature, and everyday life, making them essential for understanding everything from engineering and astronomy to art and design.

AI-generated from the Wikipedia summary — may contain errors.

Key facts

Polygon.name: Circle
Polygon.image: Circle-withsegments.svg
Polygon.caption: A circle
Polygon.symmetry: Orthogonal group|
Polygon.type: Conic section

via Wikipedia infobox

Wikidata facts

Image: Ellipsoid circular sections.gif

Show 6 more facts

Commons category: Circle geometry
Unicode character: 🔿
Stack Exchange tag: stackoverflow.com/tags/circle
Euler characteristic: 0
Commons gallery: Circle geometry
P8168: Aillon-le-Vieux

Sources (2)

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~31 min read

Article

48 sections

Contents

Terminology
Etymology
History
Symbolism and religious use
Analytic results
Circumference
Area enclosed
Radian
Equations
Cartesian coordinates
Equation of a circle
One coordinate as a function of the other
Parametric form
3-point form
Homogeneous form
Polar coordinates
Complex plane
Tangent lines
Properties
Chord
Tangent
Theorems
Inscribed angles
Sagitta
Compass and straightedge constructions
Construction with given diameter
Construction through three noncollinear points
Circle of Apollonius
Cross-ratios
{{anchor|Generalized circles}} Generalised circles
Inscription in or circumscription about other figures
Limiting case of other figures
Locus of constant sum
Squaring the circle
Generalisations
In other ''p''-norms
Topological definition
Orientation
Specially named circles
Of a triangle
Of certain quadrilaterals
Of a conic section
Of a torus
See also
Notes
References
Further reading
External links

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.