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
Woo circles
In geometry, the Woo circles, introduced by Peter Y. Woo, are a set of infinitely many Archimedean circles.
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 kn
Overlapping circles grid
An overlapping circles grid is a geometric pattern of repeating, overlapping circles of an equal radius in two-dimensional space. Commonly, designs are based on circles centered on triangles (with the
Robbins pentagon
In geometry, a Robbins pentagon is a cyclic pentagon whose side lengths and area are all rational numbers.
Homothetic center
In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contractio
Roundness
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 cyli
List of circle topics
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 l
Circle of antisimilitude
In inversive geometry, the circle of antisimilitude (also known as mid-circle) of two circles, α and β, is a reference circle for which α and β are inverses of each other. If α and β are non-intersect
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
Geodesic circle
A geodesic circle is either "the locus on a surface at a constant geodesic distance from a fixed point" or a curve of constant geodesic curvature. A geodesic disk is the region on a surface bounded by
Mrs. Miniver's problem
Mrs. Miniver's problem is a geometry problem about the area of circles. It asks how to place two circles and of given radii in such a way that the lens formed by intersecting their two interiors has e
31 great circles of the spherical icosahedron
In geometry, the 31 great circles of the spherical icosahedron is an arrangement of 31 great circles in icosahedral symmetry. It was first identified by Buckminster Fuller and is used in construction
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 u
Great-circle navigation
Great-circle navigation or orthodromic navigation (related to orthodromic course; from the Greek ορθóς, right angle, and δρóμος, path) is the practice of navigating a vessel (a ship or aircraft) along
Dividing a circle into areas
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 and diagonals, sometimes ca
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 analo
Hart circle
The Hart circle is externally tangent to and internally tangent to incircles of the associated triangles ,,, or the other way around. The Hart circle was discovered by Andrew Searle Hart. There are ei
Flattening
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblaten
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
Circumgon
In mathematics and particularly in elementary geometry, a circumgon is a geometric figure which circumscribes some circle, in the sense that it is the union of the outer edges of non-overlapping trian
Smallest-circle problem
The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, smallest enclosing circle problem) is a mathematical problem of computing the smallest circle that
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
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 circle
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, it is possible to use the key combination Alt+9676 to
Steiner chain
In geometry, a Steiner chain is a set of n circles, all of which are tangent to two given non-intersecting circles (blue and red in Figure 1), where n is finite and each circle in the chain is tangent
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 describ
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
Tangent lines to circles
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of sever
Chord (geometry)
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line se
Unit disk
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of po
Circular layout
In graph drawing, a circular layout is a style of drawing that places the vertices of a graph on a circle, often evenly spaced so that they form the vertices of a regular polygon.
Circle bundle
In mathematics, a circle bundle is a fiber bundle where the fiber is the circle . Oriented circle bundles are also known as principal U(1)-bundles. In physics, circle bundles are the natural geometric
Area of a circle
In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Johnson circles
In geometry, a set of Johnson circles comprises three circles of equal radius r sharing one common point of intersection H. In such a configuration the circles usually have a total of four intersectio
Ensō
In Zen, an ensō (円相, "circular form") is a circle that is hand-drawn in one or two uninhibited brushstrokes to express a moment when the mind is free to let the body create.
Hexafoil
The hexafoil is a design with six-fold dihedral symmetry composed from six vesica piscis lenses arranged radially around a central point, often shown enclosed in a circumference of another six lenses.
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 transfo
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 t
Circular arc
A circular arc is the arc of a circle between a pair of distinct points. If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the centre of th
Regiomontanus' angle maximization problem
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem posed by the 15th-century German mathematician Johannes Müller (also known as Regiomontanus). The probl
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
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 axi
Circle graph
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that t
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 hav
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 c
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
Ice circle
Ice discs, ice circles, ice pans, ice pancakes or ice crepes are a very rare natural phenomenon that occurs in slow moving water in cold climates. They are thin circular slabs of ice that rotate slowl
Aristotle's wheel paradox
Aristotle's wheel paradox is a paradox or problem appearing in the Greek work Mechanica, traditionally attributed to Aristotle. It states as follows: A wheel is depicted in two-dimensional space as tw
Radical axis
In 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 po
Extouch triangle
In geometry, the extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle.
Cyclic order
In mathematics, a cyclic order is a way to arrange a set of objects in a circle. Unlike most structures in order theory, a cyclic order is not modeled as a binary relation, such as "a < b". One does n
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
Limiting point (geometry)
In geometry, the limiting points of two disjoint circles A and B in the Euclidean plane are points p that may be defined by any of the following equivalent properties:
* The pencil of circles defined
Radius
In classical geometry, a radius (PL: radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from t
A Treatise on the Circle and the Sphere
A Treatise on the Circle and the Sphere is a mathematics book on circles, spheres, and inversive geometry. It was written by Julian Coolidge, and published by the Clarendon Press in 1916. The Chelsea
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 h
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
Geometry of Complex Numbers
Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geomet
Goat problem
The goat problem is either of two related problems in recreational mathematics involving at least figuratively a tethered goat (horse, bull) grazing a circular area: the interior grazing problem and t
Partial cyclic order
In mathematics, a partial cyclic order is a ternary relation that generalizes a cyclic order in the same way that a partial order generalizes a linear order.
Villarceau circles
In geometry, Villarceau circles (/viːlɑːrˈsoʊ/) are a pair of circles produced by cutting a torus obliquely through the center at a special angle. Given an arbitrary point on a torus, four circles can
Cyclically ordered group
In mathematics, a cyclically ordered group is a set with both a group structure and a cyclic order, such that left and right multiplication both preserve the cyclic order. Cyclically ordered groups we
Riemannian circle
In metric space theory and Riemannian geometry, the Riemannian circle is a great circle with a characteristic length. It is the circle equipped with the intrinsic Riemannian metric of a compact one-di
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
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 i
25 great circles of the spherical octahedron
In geometry, the 25 great circles of the spherical octahedron is an arrangement of 25 great circles in octahedral symmetry. It was first identified by Buckminster Fuller and is used in construction of
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 a