This list of circle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or concretely in physical space. It does not include metaphors like "inner circle" or "circular reasoning" in which the word does not refer literally to the geometric shape.

Geometry and other areas of mathematics

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. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...

; Circle anatomy *

Annulus (mathematics) In mathematics, an annulus (plural annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer. The word "annulus" is borrowed from the Latin word ''anulus'' or ''annulus'' meani ...

Area of a disk In geometry, the area enclosed by a circle of radius is . Here the Greek letter represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which origi ...

* Bipolar coordinates *

Central angle A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc le ...

Circular sector A circular sector, also known as circle sector or disk sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, where the smaller area is known as the ''minor sector'' and the large ...

Circular segment In geometry, a circular segment (symbol: ), also known as a disk segment, is a region of a disk which is "cut off" from the rest of the disk by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is ...

Circumference In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out ...

Concentric In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another (sharing the same center p ...

Concyclic In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle. All concyclic points are at the same distance from the center of the circle. Three points in the plane that do not all fall on a straight line ...

Degree (angle) A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. It is not an SI unit—the SI unit of angular measure is ...

Diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid f ...

Disk (mathematics) In geometry, a disk (also spelled disc). is the region in a plane bounded by a circle. A disk is said to be ''closed'' if it contains the circle that constitutes its boundary, and ''open'' if it does not. For a radius, r, an open disk is usu ...

* Horn angle * ''

Measurement of a Circle ''Measurement of a Circle'' or ''Dimension of the Circle'' (Greek: , ''Kuklou metrēsis'') is a treatise that consists of three propositions by Archimedes, ca. 250 BCE. The treatise is only a fraction of what was a longer work. Propositions Prop ...

'' * ** List of topics related to *

Pole and polar In geometry, a pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section. Polar reciprocation in a given circle is the transformation of each point in the plane into it ...

Power of a point In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle. It was introduced by Jakob Steiner in 1826. Specifically, the power \Pi(P) of a point P with respect ...

Radical axis In Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal. For this reason the radical axis is also called the power line or power bisector of the two circles. ...

Radius In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...

Radius of convergence In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or \infty. When it is positive, the power series ...

Radius of curvature In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius o ...

Sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...

Tangent lines to circles In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More ...

Versor In mathematics, a versor is a quaternion of norm one (a ''unit quaternion''). The word is derived from Latin ''versare'' = "to turn" with the suffix ''-or'' forming a noun from the verb (i.e. ''versor'' = "the turner"). It was introduced by Will ...

; Specific circles *

Apollonian circles In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. Th ...

Circles of Apollonius The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for exa ...

Archimedean circle In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes' twin circles. If the arbelos is normed such that the diameter of its outer (largest) half circle has a length of 1 and ...

* Archimedes' circles – the twin circles doubtfully attributed to Archimedes *

Archimedes' quadruplets In geometry, Archimedes' quadruplets are four congruent circles associated with an arbelos. Introduced by Frank Power in the summer of 1998, each have the same area as Archimedes' twin circles, making them Archimedean circles. Construction An ar ...

* Circle of antisimilitude *

Bankoff circle In geometry, the Bankoff circle or Bankoff triplet circle is a certain Archimedean circle that can be constructed from an arbelos; an Archimedean circle is any circle with area equal to each of Archimedes' twin circles. The Bankoff circle was fir ...

Brocard circle In geometry, the Brocard circle (or seven-point circle) is a circle derived from a given triangle. It passes through the circumcenter and symmedian of the triangle, and is centered at the midpoint of the line segment joining them (so that this ...

* Carlyle circle *

Circumscribed circle In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polyg ...

(circumcircle) :** Midpoint-stretching polygon *

Coaxal circles In geometry, Apollonian circles are two families (Pencil (geometry), pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipol ...

Director circle In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermat–Apollonius circle) is a circle consisting of all points where two perpendicular tangent lines to the ellipse or hyperbola cross each oth ...

* Fermat–Apollonius circle * Ford circle * Fuhrmann circle *

Generalised circle In geometry, a generalized circle, also referred to as a "cline" or "circline", is a straight line or a circle. The concept is mainly used in inversive geometry, because straight lines and circles have very similar properties in that geometry and ...

* GEOS circle *

Great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geome ...

Great-circle distance The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a st ...

Circle of a sphere A circle of a sphere is a circle that lies on a sphere. Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. Circles of a sphere are the spherical geometry analogs of generalised circles in Euclidean space ...

Horocycle In hyperbolic geometry, a horocycle (), sometimes called an oricycle, oricircle, or limit circle, is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction. It is the two-dimensional case of a horosph ...

Incircle and excircles of a triangle In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incen ...

Inscribed circle In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incen ...

Johnson circles In geometry, a set of Johnson circles comprises three circles of equal radius sharing one common point of intersection . In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): th ...

Magic circle (mathematics) Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298). It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diam ...

* Malfatti circles *

Nine-point circle In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: * The midpoint of ea ...

Orthocentroidal circle In geometry, the orthocentroidal circle of a non-equilateral triangle is the circle that has the triangle's orthocenter and centroid at opposite ends of its diameter. This diameter also contains the triangle's nine-point center and is a sub ...

Osculating circle In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point ''p'' on the curve has been traditionally defined as the circle passing through ''p'' and a pair of additional points on the curve i ...

* Riemannian circle * Schinzel circle *

Schoch circles In geometry, the Schoch circles are twelve Archimedean circles constructed by Thomas Schoch. History In 1979, Thomas Schoch discovered a dozen new Archimedean circles; he sent his discoveries to '' Scientific Americans "Mathematical Games" editor ...

* Spieker circle *

Tangent circles In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency: internal and external. Many problems and constructions in geometry are related to tange ...

* Twin circles *

Unit circle In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Eucli ...

* Van Lamoen circle * Villarceau circles *

Woo circles In geometry, the Woo circles, introduced by Peter Y. Woo, are a set of infinitely many Archimedean circles. Construction Form an arbelos with the two inner semicircles tangent at point ''C''. Let ''m'' denote any nonnegative real number. Dr ...

; Circle-derived entities *

Apollonian gasket In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is named after Greek ...

Arbelos In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that conta ...

Bicentric polygon In geometry, a bicentric polygon is a tangential polygon (a polygon all of whose sides are tangent to an inner incircle) which is also cyclic — that is, inscribed in an outer circle that passes through each vertex of the polygon. All tria ...

Bicentric quadrilateral In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and center of these circles are called ''inradius'' and ''circumradius'', and ''incenter'' and ''circumcenter'' r ...

Coxeter's loxodromic sequence of tangent circles In geometry, Coxeter's loxodromic sequence of tangent circles is an infinite sequence of circles arranged so that any four consecutive circles in the sequence are pairwise mutually tangent. This means that each circle in the sequence is tangent to ...

Cyclic quadrilateral In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the ''circumcircle'' or ''circumscribed circle'', and the vertices are said to be ''c ...

Cycloid In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another cu ...

Ex-tangential quadrilateral In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the ''extensions'' of all four sides are tangent to a circle outside the quadrilateral.Radic, Mirko; Kaliman, Zoran and Kadum, Vladimir, "A condition that a tan ...

Hawaiian earring In mathematics, the Hawaiian earring \mathbb is the topological space defined by the union of circles in the Euclidean plane \R^2 with center \left(\tfrac,0\right) and radius \tfrac for n = 1, 2, 3, \ldots endowed with the subspace topology: ...

Inscribed angle In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an in ...

Inscribed angle theorem In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an i ...

* Inversive distance * Inversive geometry *

Irrational rotation In the mathematical theory of dynamical systems, an irrational rotation is a map : T_\theta : ,1\rightarrow ,1\quad T_\theta(x) \triangleq x + \theta \mod 1 where ''θ'' is an irrational number. Under the identification of a circle wit ...

Lens (geometry) In 2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex). This shape can be formed as the inters ...

Lune Lune may refer to: Rivers *River Lune, in Lancashire and Cumbria, England *River Lune, Durham, in County Durham, England *Lune (Weser), a 43 km-long tributary of the Weser in Germany * Lune River (Tasmania), in south-eastern Tasmania, Australia P ...

Lune of Hippocrates In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle. Equivalently, it is a non-convex p ...

Lazy caterer's sequence The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cu ...

* Overlapping circles grid *

Pappus chain In geometry, the Pappus chain is a ring of circles between two tangent circles investigated by Pappus of Alexandria in the 3rd century AD. Construction The arbelos is defined by two circles, ''C''U and ''C''V, which are tangent at the point A a ...

Polar circle (geometry) In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is : \begin r^2 & = HA\times HD=HB\times HE=HC\times HF \\ & =-4R^2\cos A \cos B \cos C=4R^2-\frac(a^2+b^2+c^2), \end ...

Power center (geometry) In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical axes of the pairs of circles. If the radical center lies outside of all three circles, then it is the center of th ...

* Salinon *

Semicircle In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, radians, or a half-turn). It has only one line o ...

Squircle A squircle is a shape intermediate between a square and a circle. There are at least two definitions of "squircle" in use, the most common of which is based on the superellipse. The word "squircle" is a portmanteau of the words "square" and "ci ...

Steiner chain In geometry, a Steiner chain is a set of circles, all of which are tangent to two given non-intersecting circles (blue and red in Figure 1), where is finite and each circle in the chain is tangent to the previous and next circles in the chain. ...

Tangential polygon In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an ''incircle''). This is a circle that is tangent to each of the polygon's sides. The dual pol ...

Tangential quadrilateral In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral. This circle is called the ...

:; Roulettes :* Centered trochoid :*

Epitrochoid In geometry, an epitrochoid ( or ) is a roulette traced by a point attached to a circle of radius rolling around the outside of a fixed circle of radius , where the point is at a distance from the center of the exterior circle. The parametric ...

::*

Epicycloid In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an ''epicycle''—which rolls without slipping around a fixed circle. It is a particular kind of roulette. Equati ...

::*

Cardioid In geometry, a cardioid () is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal ...

::*

Nephroid In geometry, a nephroid () is a specific plane curve. It is a type of epicycloid in which the smaller circle's radius differs from the larger by a factor of one-half. Name Although the term ''nephroid'' was used to describe other curves, it was ...

::*

Deferent and epicycle In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (, meaning "circle moving on another circle") was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, S ...

Hypotrochoid In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius rolling around the inside of a fixed circle of radius , where the point is a distance from the center of the interior circle. The parametric equations f ...

::*

Hypocycloid In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid cre ...

::*

Astroid In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle as it rolls inside a fixed circle with four times the radius. By double generation, it ...

::*

Deltoid curve In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the insid ...

:; Topology :*

Borromean rings In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the t ...

Circle bundle In mathematics, a circle bundle is a fiber bundle where the fiber is the circle S^1. Oriented circle bundles are also known as principal ''U''(1)-bundles. In physics, circle bundles are the natural geometric setting for electromagnetism. A circ ...

Quasicircle In mathematics, a quasicircle is a Jordan curve in the complex plane that is the image of a circle under a quasiconformal mapping of the plane onto itself. Originally introduced independently by and , in the older literature (in German) they were ...

; Circle-related theory * Apollonius' problem ** Limiting cases of Apollonius' problem *

Belt problem The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radius ''r''1 and ''r''2 whose centers are separated by a distance ''P''. The solution of the belt problem requ ...

Benz plane In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split ...

Bertrand's paradox (probability) The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work ''Calcul des probabilités'' (1889), as an example to show that the principle of indifference may not produce de ...

Bonnesen's inequality Bonnesen's inequality is an inequality (mathematics), inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetry, isoperimetric ine ...

Brahmagupta's formula In Euclidean geometry, Brahmagupta's formula is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides; its generalized version (Bretschneider's formula) can be used with non-cyclic ...

Buffon's needle problem In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: :Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floo ...

* Bundle theorem *

Butterfly theorem The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows:Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publ., 2007 (orig. 1929). Let be the midpoint of a chord of a circle, through which ...

* Carnot's theorem *

Casey's theorem In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey. Formulation of the theorem Let \,O be a circle of radius \,R. Let \,O_1, O_2 ...

* Circle graph *

Circle map In mathematics, particularly in dynamical systems, Arnold tongues (named after Vladimir Arnold) Section 12 in page 78 has a figure showing Arnold tongues. are a pictorial phenomenon that occur when visualizing how the rotation number of a dynamic ...

Circle packing In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated '' packing de ...

** Circle packing in a circle **

Circle packing in an equilateral triangle Circle packing in an equilateral triangle is a packing problem in discrete mathematics where the objective is to pack unit circles into the smallest possible equilateral triangle. Optimal solutions are known for and for any triangular number of ...

** Circle packing in an isosceles right triangle **

Circle packing theorem The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles (in gen ...

** '' Introduction to Circle Packing'' – a book by Kenneth Stephenson * Circular surface * Clifford's circle theorems * Compass and straightedge **

Mohr–Mascheroni theorem In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone. It must be understood that by "any geometric construction", we are refer ...

** Poncelet–Steiner theorem *

Descartes' theorem In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mu ...

* Dinostratus' theorem *

Dividing a circle into areas The number of and for first 6 terms of Moser's circle problem In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with ''n'' sides in such a way as to ''maximise'' the number of areas created by the edges an ...

Equal incircles theorem In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of rays are drawn from a given point to a given line such that the inscribed circles of the triangles formed by adjacent ...

* Five circles theorem * Gauss circle problem * Gershgorin circle theorem *

Geometrography In the mathematical field of geometry, geometrography is the study of geometrical constructions. The concepts and methods of geometrography were first expounded by Émile Lemoine (1840–1912), a French civil engineer and a mathematician, in a m ...

Hadamard three-circle theorem In complex analysis, a branch of mathematics, the Hadamard three-circle theorem is a result about the behavior of holomorphic functions. Let f(z) be a holomorphic function on the annulus :r_1\leq\left, z\ \leq r_3. Let M(r) be the maximum of , f ...

Hardy–Littlewood circle method In mathematics, the Hardy–Littlewood circle method is a technique of analytic number theory. It is named for G. H. Hardy and J. E. Littlewood, who developed it in a series of papers on Waring's problem. History The initial idea is usually at ...

Isoperimetric problem In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname(S) of a set S\subset\R^n by ...

Japanese theorem for cyclic polygons __notoc__ In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant.Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publ., 2007 (orig. 1929). Conversel ...

Japanese theorem for cyclic quadrilaterals In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Triangulating an arbitrary cyclic quadrilateral by its diagonals yields four overlapping t ...

Kosnita's theorem In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle. Let ABC be an arbitrary triangle, O its circumcenter and O_a,O_b,O_c are the circumcenters of three triangles OBC, OCA, and OAB resp ...

* Lester's theorem * Milne-Thomson circle theorem *

Miquel's theorem Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles ...

Monge's theorem In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinea ...

* Mrs. Miniver's problem * Pivot theorem *

Pizza theorem In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because it mimics a traditional pizza slicing technique. It shows that if two people sha ...

* Squaring the circle *

Poncelet's porism In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed figure, inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygo ...

Ptolemy's theorem In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician ...

Ptolemy's table of chords The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's ''Almagest'', a treatise on mathematical astronomy. It ...

* Regiomontanus' angle maximization problem * Ring lemma * Seven circles theorem * Six circles theorem *

Smallest circle problem The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a mathematical problem of computing the smallest circle that contains all o ...

Tammes problem In geometry, the Tammes problem is a problem in packing a given number of circles on the surface of a sphere such that the minimum distance between circles is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the n ...

Tarski's circle-squaring problem Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area. This was proven to be possible by Mikl ...

Thales' theorem In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, the angle ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved ...

; Circle tangents in non-geometric theory *

Circle criterion In nonlinear control and stability theory, the circle criterion is a stability criterion for nonlinear time-varying systems. It can be viewed as a generalization of the Nyquist stability criterion In control theory and stability theory, the Nyq ...

* Circle group **

Group of rational points on the unit circle In mathematics, the rational points on the unit circle are those points (''x'', ''y'') such that both ''x'' and ''y'' are rational numbers ("fractions") and satisfy ''x''2 + ''y''2 = 1. The set of such points turns out to ...

Circular algebraic curve In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation ''F''(''x'', ''y'') = 0, where ''F'' is a polynomial with real coefficients and the highest-order terms of ''F'' form a polynomial d ...

Circular distribution In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range A circular distribution is often a continuous probability ...

Circular statistics Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, R''n''), axes ( lines through the origin in R''n'') or rotations in R''n''. Mo ...

* Mean of circular quantities *

Polygon-circle graph In the mathematical discipline of graph theory, a polygon-circle graph is an intersection graph of a set of convex polygons all of whose vertices lie on a common circle. These graphs have also been called spider graphs. This class of graphs was ...

* Splitting circle method *

von Mises distribution In probability theory and directional statistics, the von Mises distribution (also known as the circular normal distribution or Tikhonov distribution) is a continuous probability distribution on the circle. It is a close approximation to the w ...

Wigner semicircle distribution The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution on minus;''R'', ''R''whose probability density function ''f'' is a scaled semicircle (i.e., a semi-ellipse) centered at (0, 0): :f(x)=\sq ...

Wrapped distribution In probability theory and directional statistics, a wrapped probability distribution is a continuous probability distribution that describes data points that lie on a unit ''n''-sphere. In one dimension, a wrapped distribution consists of points on ...

Wrapped Cauchy distribution In probability theory and directional statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping" of the Cauchy distribution around the unit circle. The Cauchy distribution is sometimes known a ...

Wrapped normal distribution In probability theory and directional statistics, a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping" of the normal distribution around the unit circle. It finds application in the theory of Brownia ...

; Other topics * Thomas Baxter (mathematician)

Physical sciences and engineering

Centrifugal force In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parall ...

* Centripetal force *

Circle of confusion In optics, a circle of confusion (CoC) is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as disk of confusion, circle of indistinctness, blur circle, or ...

Circle of forces The circle of forces, traction circle, friction circle, or friction ellipse is a useful way to think about the dynamic interaction between a vehicle's tire and the road surface. The diagram below shows the tire from above, so that the road surface ...

* Circular dichroism * Circular orbit *

Mohr's circle Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineer ...

* Non-uniform circular motion *

Thomson problem The objective of the Thomson problem is to determine the minimum electrostatic potential energy configuration of electrons constrained to the surface of a unit sphere that repel each other with a force given by Coulomb's law. The physicist J. J. ...

Uniform circular motion In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rot ...

Geography

* Arctic Circle *

Antarctic Circle The Antarctic Circle is the most southerly of the five major circles of latitude that mark maps of Earth. The region south of this circle is known as the Antarctic, and the zone immediately to the north is called the Southern Temperate Zone. So ...

Circle of latitude A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth (ignoring elevation) at a given latitude coordinate line. Circles of latitude are often called parallels because ...

* Equator *

Polar circle A polar circle is a geographic term for a conditional circular line (arc) referring either to the Arctic Circle or the Antarctic Circle. These are two of the keynote circles of latitude (parallels). On Earth, the Arctic Circle is currently d ...

* Position circle *

Tropic of Cancer The Tropic of Cancer, which is also referred to as the Northern Tropic, is the most northerly circle of latitude on Earth at which the Sun can be directly overhead. This occurs on the June solstice, when the Northern Hemisphere is tilted tow ...

Tropic of Capricorn The Tropic of Capricorn (or the Southern Tropic) is the circle of latitude that contains the subsolar point at the December (or southern) solstice. It is thus the southernmost latitude where the Sun can be seen directly overhead. It also reac ...

Artifacts

* Addendum circle *

Center pivot irrigation Center-pivot irrigation (sometimes called central pivot irrigation), also called water-wheel and circle irrigation, is a method of crop irrigation in which equipment rotates around a pivot and crops are watered with sprinklers. A circular area ...

Circular ditches Approximately 120–150 Neolithic earthworks enclosures are known in Central Europe. They are called ''Kreisgrabenanlagen'' ("circular ditched enclosures") in German, or alternatively as roundels (or "rondels"; German ''Rondelle''; so ...

Circular slide rule The slide rule is a mechanical analog computer which is used primarily for multiplication and division, and for functions such as exponents, roots, logarithms, and trigonometry. It is not typically designed for addition or subtraction, which i ...

Compass (drafting) A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses ...

Crop circle A crop circle, crop formation, or corn circle is a pattern created by flattening a crop, usually a cereal. The term was first coined in the early 1980s by Colin Andrews. Crop circles have been described as all falling "within the range of the ...

* Dip circle *

List of gear nomenclature This page lists the standard US nomenclature used in the description of mechanical gear construction and function, together with definitions of the terms. The terminology was established by the American Gear Manufacturers Association (AGMA), unde ...

* Peaucellier–Lipkin linkage *

Pitch circle This page lists the standard US nomenclature used in the description of mechanical gear construction and function, together with definitions of the terms. The terminology was established by the American Gear Manufacturers Association (AGMA), unde ...

Repeating circle Developed from the reflecting circle, the repeating circle is an instrument for geodetic surveying, invented by Etienne Lenoir in 1784, while an assistant of Jean-Charles de Borda, who later improved the instrument. It was notable as being the ...

Timber circle In archaeology, timber circles are rings of upright wooden posts, built mainly by ancient peoples in the British Isles and North America. They survive only as gapped rings of post-holes, with no evidence they formed walls, making them distinct fr ...

Traffic circle A roundabout is a type of circular intersection or junction in which road traffic is permitted to flow in one direction around a central island, and priority is typically given to traffic already in the junction.''The New Shorter Oxford Eng ...

** List of circles in Washington, D.C. **

List of traffic circles in New Jersey This is a list of traffic circles in New Jersey. The U.S. state of New Jersey at one point had a total of 101 traffic circles, 44 of which were part of State highway, state roads. However, the number has shrunk as traffic circles have been phas ...

Setting circles Setting circles are used on telescopes equipped with an equatorial mount to find astronomical objects in the sky by their equatorial coordinates often used in star charts or ephemerides. Description Setting circles consist of two graduated disk ...

* Stone circle * Wheel

Glyphs and symbols

* Circled dot (disambiguation) * Circles in Polish mythology *

Crescent A crescent shape (, ) is a symbol or emblem used to represent the lunar phase in the first quarter (the "sickle moon"), or by extension a symbol representing the Moon itself. In Hinduism, Lord Shiva is often shown wearing a crescent moon on his ...

Dotted circle The dotted circle, in Unicode, is a typographic character used to illustrate the effect of a combining mark, such as a diacritic mark. In Windows Windows is a group of several proprietary graphical operating system families developed and ma ...

* Enso *

Magic circle A magic circle is a circle of space marked out by practitioners of some branches of ritual magic, which they generally believe will contain energy and form a sacred space, or will provide them a form of magical protection, or both. It may be mark ...

Olympic emblem Each Olympic Games has its own Olympic emblem, which is a design integrating the Olympic rings with one or more distinctive elements. They are created and proposed by the Organising Committee of the Olympic Games (OCOG) or the National Olympic Comm ...

Ouroboros The ouroboros or uroboros () is an ancient symbol depicting a serpent or dragon eating its own tail. The ouroboros entered Western tradition via ancient Egyptian iconography and the Greek magical tradition. It was adopted as a symbol in Gnost ...

Petosiris to Nechepso __notoc__ Petosiris to Nechepso is a letter describing an ancient divination technique using numerology and a diagram. It is likely to be a pseudepigraph. Petosiris and Nechepso are considered to be the founders of astrology in some traditions. ...

* Quatrefoil *

Ring (diacritic) A ring diacritic may appear above or below letters. It may be combined with some letters of the extended Latin alphabets in various contexts. Rings Distinct letter The character Å (å) is derived from an A with a ring. It is a distinct le ...

Roundel A roundel is a circular disc used as a symbol. The term is used in heraldry, but also commonly used to refer to a type of national insignia used on military aircraft, generally circular in shape and usually comprising concentric rings of diff ...

Sacred Chao Discordianism is a religion, philosophy, or paradigm centered on Eris (mythology), Eris, a.k.a. Discordia, the Goddess of chaos. Discordianism uses archetypes or ideals associated with her. It was founded after the 1963 publication of its "holy ...

* Shield of the Trinity *

Solar symbol A solar symbol is a symbol representing the Sun. Common solar symbols include circles (with or without rays), crosses, and spirals. In religious iconography, personifications of the Sun or solar attributes are often indicated by means of a hal ...

s * Squared-circle postmark *

Sun cross A sun cross, solar cross, or wheel cross is a solar symbol consisting of an equilateral cross inside a circle. The design is frequently found in the symbolism of prehistoric cultures, particularly during the Neolithic to Bronze Age periods of ...

* Symbol of Tanit *

Trefoil A trefoil () is a graphic form composed of the outline of three overlapping rings, used in architecture and Christian symbolism, among other areas. The term is also applied to other symbols with a threefold shape. A similar shape with four ring ...

Triquetra The triquetra ( ; from the Latin adjective ''triquetrus'' "three-cornered") is a triangular figure composed of three interlaced arcs, or (equivalently) three overlapping '' vesicae piscis'' lens shapes. It is used as an ornamental design in ar ...

Vesica piscis The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other. In Latin, "vesica piscis" litera ...

* Triple Goddess symbol *

Yin and yang Yin and yang ( and ) is a Chinese philosophical concept that describes opposite but interconnected forces. In Chinese cosmology, the universe creates itself out of a primary chaos of material energy, organized into the cycles of yin and ya ...

Geometry and other areas of mathematics

Physical sciences and engineering

Geography

Artifacts

Glyphs and symbols

See also