List of circle topics
From HandWiki
Short description: none
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 anatomy
- Annulus (mathematics) – Region between two concentric circles
- Area of a disk
- Bipolar coordinates – 2-dimensional orthogonal coordinate system based on Apollonian circles
- Central angle – Measure of two radii meeting
- Circular sector – Portion of a disk enclosed by two radii and an arc
- Circular segment – Area bounded by a circular arc and a straight line
- Circumference
- Concentric
- Concyclic
- Degree (angle) – Unit of plane angle where a full circle equals 360°
- Diameter – Straight line segment that passes through the centre of a circle
- Disk (mathematics) – Plane figure, bounded by circle
- Horn angle – Type of curvilinear angle
- Measurement of a Circle
- π – Number, approximately 3.14
- List of topics related to π – Wikipedia list article
- Pole and polar
- Power of a point – Relative distance of a point from a circle
- Radical axis – All points whose relative distances to two circles are same
- Radius – Segment in a circle or sphere from its center to its perimeter or surface and its length
- Radius of convergence – Domain of convergence of power series
- Radius of curvature
- Sphere – Set of points equidistant from a center
- Tangent lines to circles – Line which touches a circle at exactly one point
- Versor – Quaternion of norm 1 (unit quaternion)
- Specific circles
- Apollonian circles – Circles in two perpendicular families
- Circles of Apollonius – Several sets of circles associated with Apollonius of Perga
- Archimedean circle
- Archimedes' circles – the twin circles doubtfully attributed to Archimedes
- Archimedes' quadruplets
- Circle of antisimilitude
- Bankoff circle
- Brocard circle
- Carlyle circle – Circle associated with a quadratic equation
- Circumscribed circle (circumcircle)
- Coaxal circles
- Director circle – Circle formed by all 90° crossings of tangents of an ellipse or hyperbola
- Fermat–Apollonius circle
- Ford circle – Rational circle tangent to the real line
- Fuhrmann circle
- Generalised circle – Concept in geometry including line and circle
- GEOS circle
- Great circle – Spherical geometry analog of a straight line
- Great-circle distance – Shortest distance between two points on the surface of a sphere
- Circle of a sphere – Mathematical expression of circle like slices of sphere
- Horocycle
- Incircle and excircles of a triangle – Circles tangent to all three sides of a triangle
- Inscribed circle
- Johnson circles – Geometric theorem regarding 3 circles intersecting at a point
- Magic circle (mathematics) – Chinese mathematical arrangement
- Malfatti circles – Three tangent circles in a triangle
- Nine-point circle
- Orthocentroidal circle
- Osculating circle – Circle of immediate corresponding curvature of a curve at a point
- Riemannian circle – Great circle with a characteristic length
- Schinzel circle
- Schoch circles
- Spieker circle
- Tangent circles – Circles related to a point in the plane
- Taylor circle
- Twin circles
- Unit circle – Circle with radius of one
- Van Lamoen circle
- Villarceau circles – Intersection of a torus and a plane
- Woo circles
- Circle-derived entities
- Apollonian gasket – Fractal composed of tangent circles
- Arbelos
- Bicentric polygon
- Bicentric quadrilateral – Type of shape
- Coxeter's loxodromic sequence of tangent circles – Circle packing
- Cyclic quadrilateral – Quadrilateral whose vertices can all fall on a single circle
- Cycloid
- Ex-tangential quadrilateral
- Hawaiian earring – Topological space defined by the union of circles
- Inscribed angle – Angle formed in the interior of a circle
- Inscribed angle theorem
- Inversive distance
- Inversive geometry
- Irrational rotation – Rotation of a circle by an angle of π times an irrational number
- Lens (geometry) – Convex plane region bounded by two circular arcs
- Lune
- Lune of Hippocrates – Geometric construction
- Lazy caterer's sequence – Counts pieces of a disk cut by lines
- Overlapping circles grid – Geometric pattern used in art
- Pappus chain – Ring of circles between two tangent circles
- Polar circle (geometry)
- Power center (geometry) – For 3 circles, the intersection of the radical axes of each pair
- Salinon
- Semicircle
- Squircle
- Steiner chain – Set of circles related by tangency
- Tangential polygon
- Tangential quadrilateral
- Roulettes
- Centered trochoid – Geometric curve
- Epitrochoid
- Epicycloid – Plane curve traced by a point on a circle rolled around another circle
- Cardioid
- Nephroid
- Deferent and epicycle
- Topology
- Borromean rings – Three linked but pairwise separated rings
- Circle bundle – Principal fiber bundle
- Quasicircle
- Circle-related theory
- Apollonius' problem – Construct circles that are tangent to three given circles in a plane
- Belt problem
- Benz plane – Geometrical structure
- Bertrand's paradox (probability)
- Bonnesen's inequality – Relates the length, area and radius of the incircle and the circumcircle of a Jordan curve
- Brahmagupta's formula – Formula relating the area of a cyclic quadrilateral to its side lengths
- Buffon's needle problem
- Bundle theorem
- Butterfly theorem – About the midpoint of a chord of a circle, through which two other chords are drawn
- Carnot's theorem – Gives the sum of the distances from the circumcenter to the sides of an arbitrary triangle
- Casey's theorem – On four non-intersecting circles that lie inside a bigger circle and tangent to it
- Circle graph – Intersection graph of a chord diagram
- Circle map
- Circle packing – Field of geometry closely arranging circles on a plane
- Circle packing in a circle – Two-dimensional packing problem
- Circle packing in an equilateral triangle – Two-dimensional packing problem
- Circle packing in an isosceles right triangle – Two-dimensional packing problem
- Circle packing theorem – Describes the possible tangency relations between circles with disjoint interiors
- Introduction to Circle Packing – a book by Kenneth Stephenson
- Circular surface
- Clifford's circle theorems – A sequence of theorems relating to sets of circles intersecting at a common point
- Compass and straightedge
- Mohr–Mascheroni theorem – Constructions performed by a compass and straightedge can be performed by a compass alone
- Poncelet–Steiner theorem – Universality of construction using just a straightedge and a single circle with center
- Descartes' theorem – Equation for radii of tangent circles
- Dinostratus' theorem
- Dividing a circle into areas – Problem in geometry
- Equal incircles theorem – On rays from a point to a line, with equal inscribed circles between adjacent rays
- Five circles theorem – Derives a pentagram from five chained circles centered on a common sixth circle
- Gauss circle problem – How many integer lattice points there are in a circle
- Gershgorin circle theorem – Bound on eigenvalues
- Geometrography
- Goat grazing problem – Recreational mathematics planar boundary and area problem
- Hadamard three-circle theorem
- Hardy–Littlewood circle method
- Isoperimetric problem – Geometric inequality which sets a lower bound on the surface area of a set given its volume
- Japanese theorem for cyclic polygons – Theorem in Euclidean geometry
- Japanese theorem for cyclic quadrilaterals – Centers of the incircles of triangles inside a cyclic quadrilateral form a rectangle
- Kosnita's theorem – Concurrency of lines connecting to certain circles associated with an arbitrary triangle
- Lester's theorem – Several points associated with a scalene triangle lie on the same circle
- Milne-Thomson circle theorem
- Miquel's theorem – Concerns 3 circles through triples of points on the vertices and sides of a triangle
- Monge's theorem – The intersections of the 3 pairs of external tangent lines to 3 circles are collinear
- Mrs. Miniver's problem – Problem on areas of intersecting circles
- Pivot theorem – Concerns 3 circles through triples of points on the vertices and sides of a triangle
- Pizza theorem – Equality of areas of a sliced disk
- Squaring the circle – Problem of constructing equal-area shapes
- Poncelet's porism
- Ptolemy's theorem – Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
- Ptolemy's table of chords – 2nd century AD trigonometric table
- Regiomontanus' angle maximization problem – Famous mathematical optimization problem
- Ring lemma
- Seven circles theorem – About a chain of six circles tangent to a seventh circle and each to its 2 neighbors
- Six circles theorem – Relates to a chain of six circles together with a triangle
- Smallest circle problem
- Tammes problem – Circle-packing on the surface of a sphere
- Tarski's circle-squaring problem – Problem of cutting and reassembling a disk into a square
- Thales' theorem
- Circle tangents in non-geometric theory
- Circle criterion
- Circle group – Lie group of complex numbers of unit modulus; topologically a circle
- Circular algebraic curve
- Circular distribution – Type of probability distribution
- Circular statistics
- Mean of circular quantities
- Polygon-circle graph – Intersection graph of convex polygons whose vertices lie on a common circle
- Splitting circle method
- von Mises distribution – Probability distribution on the circle
- Wigner semicircle distribution
- Wrapped distribution
- Other topics
- Thomas Baxter (mathematician)
Physical sciences and engineering
- Centrifugal force
- Centripetal force
- Circle of confusion
- Circle of forces
- Circular dichroism
- Circular orbit
- Mohr's circle
- Non-uniform circular motion
- Thomson problem – Max distance configuration for N points on a sphere
- Uniform circular motion
Geography
- Circle of latitude
- Great-circle distance – Shortest distance between two points on the surface of a sphere
- Position circle
Artifacts
- Addendum circle
- Belt problem
- Center pivot irrigation – Method of crop irrigation
- Circular ditches
- Circular slide rule
- Compass (drafting)
- Crop circle – Pattern in a crop field
- Dip circle
- List of gear nomenclature
- Peaucellier–Lipkin linkage – Mechanical linkage capable of transforming rotary motion into linear motion
- Pitch circle
- Repeating circle
- Timber circle
- Traffic circle
- Setting circles
- Stone circle
- Wheel
Glyphs and symbols
- Borromean rings – Three linked but pairwise separated rings
- Circled dot (disambiguation)
- Circles in Polish mythology
- Crescent – Symbol of a lunar phase
- Dotted circle – Non-significant typographic character
- Ensō – Japanese motif
- Magic circle
- Olympic emblem
- Ouroboros – Symbolic serpent with its tail in its mouth
- Petosiris to Nechepso
- Quatrefoil – Artistic representation of four circular leaf shapes used in architecture
- Ring (diacritic)
- Roundel – Identification symbol, commonly used in aircraft insignia and heraldry, usually of circular design
- Sacred Chao
- Shield of the Trinity
- Solar symbols
- Squared-circle postmark
- Sun cross
- Symbol of Tanit
- Trefoil – Artistic representation of three circular leaf shapes used in architecture
- Triquetra – Triangular motif formed of three interlaced arcs or loops
- Vesica piscis
- Triple Goddess symbol
- Yin and yang
See also
 |  |
