Circles

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.

[[File:Circle-withsegments.svg|thumb|right|Circle with

projection of the Earth's equator out into space

plane figure, bounded by circle

geometric line segment whose endpoints both lie on the curve

intersection of the sphere and a plane which passes through the center point of the sphere

circle with radius one

portion of a disk enclosed by two radii and an arc

object movement along a circular path

pattern in a crop field

[[File:Circle-withsegments.svg|thumb|

great circle passing through the celestial poles, the zenith, and the nadir of a particular location

slice of a circle cut perpendicular to the radius

geometric surface defined by two concentric circles

thumb|right|200px |A circle of radius compressed to an ellipse. thumb|right|200px |A sphere of radius compressed to an oblate ellipsoid of revolution.

abstract illustrative organization of color hues

measure of two radii meeting

circular work of art

geometric engineering calculation technique

segment of a circle

thumb| () by Kanjuro Shibata XX. Some artists draw with an opening in the circle, while others close the circle. In Zen art, an is a circle hand-drawn in one or two uninhibited brushstrokes to express the Zen mind, which is associated with enlightenment, emptiness, freedom, and the state of no-mind.

shape bounded by arcs of two circles whose area is a rational multiple of the circles' radii

line determined by two circles

a family of circles where every one intersects every circle in a second family of circles orthogonally

region on world map with more people inside than outside

construction in geometry, which, given to a conic, associates a line (“polar”) to a point and a point (“pole”) to a line

set of points at distance less than one from a given point

circle of immediate corresponding curvature of a curve at a point

Part of celestial coordinate system

thumb|right|The Flag of France|Tricolore cockade of the [[French Air Force was first used on military aircraft before the First World War]]

area enclosed by a circle

method of crop irrigation

line which touches a circle at exactly one point

problem of counting integer points within a circle of given radius centered at the origin

right|150px|thumb|Two simple diagrams of the unknot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied into it, unknotted. To a knot theorist, an unknot is any embedded topological circle in the 3-sphere that is ambient isotopic (that is, deformable) to a geometrically round circle, the standard unknot.

paradox

cyclic sequence of circles, each tangent to its two neighbors in the sequence and to two fixed circles

apparent absurdity in rolling a coin along its edge

big circular ice floe (ca 1 m ... 50 m diameter) rotating on a river

Shape produced by intersection of a torus

great circle perpendicular to the mathematical horizon

knitting of tubular shapes using knitting needles or a circular knitting machine

point from which at least two geometrically similar figures can be seen as a dilation/contraction of one another

geometric theorem regarding 3 circles intersecting at a point

ternary relation that is cyclic (if [𝑥,𝑦,𝑧] then [𝑧,𝑥,𝑦]), asymmetric (if [𝑥,𝑦,𝑧] then not [𝑧,𝑦,𝑥]), transitive (if [𝑤,𝑥,𝑦] and [𝑤,𝑦,𝑧] then [𝑤,𝑥,𝑧]) and connected (for distinct 𝑥,𝑦,𝑧, either [𝑥,𝑦,𝑧] or [𝑧,𝑥,𝑦])

mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane

Circles of Apollonius

mathematical problem

famous mathematical optimization problem

two circles with only one common point

Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle. Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing. In geometric dimensioning and tolerancing, control of a cylinder can also include its fidelity to the longitudinal axis, yielding cylindricity. The analogue of roundness in three dimensions (that is, for spheres) is sphericity.

dotted circle (U+25CC); note that the reference glyph is intentionally larger than the glyph used in the UCS standard to indicate combining characters

a type of node-link graph in which vertices represent chords of a circle and edges represent crossings

curve that is a circle or a straight line

cyclic pentagon whose side lengths and area are all rational numbers

thumb|A geometrical hexafoil

fiber bundle whose fibers are circles