circle
Sign in to saveA 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
Article
48 sectionsContents
- 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
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.