n
(geometry) In a plane, the two imaginary circular points at infinity; in space of three dimensions, the imaginary circle at infinity.
n
(geometry) The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative.
n
(geometry, uncountable) The branch of geometry dealing with what can be deduced in Euclidean geometry when the notions of line length and angle size are ignored.
n
(mathematics) a vector space having no origin
adj
(geometry) Said of a set of points in an affine space: the property that the vectors issuing from an arbitrarily chosen point to the rest of the points are linearly independent.
n
(mathematics, physics) A form of complex null geodesic
n
(mathematics) A cubic curve of the form xy² + ey = ax³ + bx² + cx + d
n
A Lorentzian manifold in Minkowski space which is the analogue of a hyperbola in ordinary Euclidean space.
n
A heterosquare in which the sums form a sequence of consecutive numbers.
adj
(geometry) Orthogonal under the polar pairing between the symmetric algebra of a vector space and its dual.
n
Abbreviation of arccosine. [(trigonometry) Any of several single-valued or multivalued functions that are inverses of the cosine function.]
n
(trigonometry) function that is the compositional inverse of the cosecant function. Symbol: arccsc
n
(mathematics) Alternative form of arcosh (“the inverse hyperbolic cosine function”) [(trigonometry) The area hyperbolic cosine function, i.e., the inverse hyperbolic cosine function.]
n
(trigonometry) Any of several single-valued or multivalued functions that are inverses of the cosine function.
n
(trigonometry) An inverse of the cotangent function. Symbol: arccot
n
(mathematics) Alternative form of arcoth (“the area hyberbolic cotangent function, i.e., the inverse hyperbolic cotangent function.”) [(trigonometry) The area hyperbolic cotangent function, i.e., the inverse hyperbolic cotangent function.]
n
(mathematics, chiefly historical) Synonym of pi
n
(trigonometry) The area hyperbolic cosine function, i.e., the inverse hyperbolic cosine function.
n
(trigonometry) The area hyperbolic cotangent function, i.e., the inverse hyperbolic cotangent function.
n
(trigonometry) The area hyperbolic cosecant function, i.e., the inverse hyperbolic cosecant function.
n
(trigonometry) function that is the compositional inverse of the secant function. Symbol: arcsec
n
(trigonometry) Alternative form of arsech (“the inverse hyberbolic secant function”) [(trigonometry) The area hyperbolic secant function, i.e., the inverse hyperbolic secant function.]
n
Abbreviation of arcsine. [(trigonometry) Any of several single-valued or multivalued functions that are inverses of the sine function. Symbol: arcsin, sin⁻¹]
n
(trigonometry) Any of several single-valued or multivalued functions that are inverses of the sine function. Symbol: arcsin, sin⁻¹
n
(trigonometry) Alternative form of arsinh (“the inverse hyperbolic sine function”) [(trigonometry) The area hyperbolic sine function, i.e., the inverse hyperbolic sine function.]
n
(trigonometry) Any of several single-valued or multivalued functions that are inverses of the tangent function. Symbol: arctan, tan⁻¹
n
(trigonometry) Alternative form of artanh (“the inverse hyberbolic tangent function”) [(trigonometry) The area hyperbolic tangent function, i.e., the inverse hyperbolic tangent function.]
n
(mathematics) A chaotic map from the torus into itself.
n
(trigonometry) The area hyperbolic secant function, i.e., the inverse hyperbolic secant function.
n
(mathematics) The set of points in a metric space of any number of dimensions lying within a given distance (the radius) of a given point.
n
(mathematics) A curve with formula x⁴+x²ʸ²+y⁴=x(x²+y²),.
n
A measure of relative power, defined as log₁₀(P ₁/P ₂), where P₁ and P₂ are the measured and reference power respectively.
adj
(mathematics) Composed of a pair of complex numbers having certain defined properties
adj
Of or pertaining to interpolation in two dimensions using cubic splines or other polynomials (technique for sharpening enlargements of digital images).
adj
(mathematics) Used to describe a curve composed of two moving points; e.g. a hyperbola.
n
(mathematics) A polydisc of the second order
adj
(geometry, of a curve) Being a branched double cover of an elliptic curve.
n
(geometry) The second plurigenus P₂ of a surface.
n
(number theory, mathematics) A magic square that remains magic when all of its numbers are replaced by their squares.
adj
(geometry, of a map) Being a regular map with regular inverse.
n
(mathematics) An extension of the least squares method that removes or downweights extreme outliers
n
(mathematics) A line that is tangent to a curve at two points
adj
(geometry) Meeting a curve at the tangency points of its bitangents.
n
(topology, complex analysis) A curve in the complex plane such that it is possible to define a single analytic branch of a multi-valued function on the plane minus that curve.
n
(geometry, crystallography) An infinite array of discrete points generated by a set of discrete translation operations mathbf R=n_1 mathbf a₁+n_2 mathbf a₂+n_3 mathbf a₃, where nᵢ are any integers and aᵢ are known as the primitive vectors which lie in different directions and span the lattice.
n
(mathematics, number theory) In the theory of magic squares, a set of n cells forming two parallel diagonal lines in the square.
n
Synonym of Calabi-Yau manifold
n
(mathematics) Euclidean space described by Cartesian coordinates.
n
(geometry) A development of the method of indivisibles, dealing with two-dimensional area or three-dimensional volume based on the intersections of lines or planes surrounding a region. It was an early step toward integral calculus.
n
(mathematics) A variety associated to a hypersurface.
n
(mathematics) A theorem about triangles in plane geometry, regards the ratio of the side lengths of a triangle divided by cevians.
n
(mathematics) A metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension.
n
(topology) A mathematical construction based on this pattern of squares
n
(trigonometry) Synonym of trigonometric function
n
(mathematics) A plane curve whose curvature at any point is proportional to distance along it.
n
(trigonometry) the hacoversed sine
n
(mathematics) The dual of a line.
v
(mathematics) To write a quadratic polynomial in terms of the square of a binomial.
n
(mathematics) A square matrix C with 0 on the diagonal and +1 and −1 off the diagonal, such that CᵀC is a multiple of the identity matrix I.
n
(geometry) The study of conformal (angle-preserving) transformations on a space;
adj
(of a complex number) Such that the line segment joining it to the origin can be constructed using only a pair of compasses and a straightedge.
n
(mathematics) The n-dimensional space contained by an n-dimensional polytope (called volume in the case of a polyhedron and area in the case of a polygon); length, area or volume, generalized to an arbitrary number of dimensions.
n
(mathematics) Any of a group of elements of a type of four-dimensional vector space
adj
(mathematics) Of or pertaining to coquaternions
n
(mathematics) Any of four points on the common chord of a cubic curve intercepted by a cone
n
(trigonometry) In a right triangle, the reciprocal of the sine of an angle. Symbols: cosec, csc
n
(trigonometry) In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse. Symbol: cos
n
(trigonometry) law of cosines
n
(trigonometry) law of cosines
n
(trigonometry) Synonym of cosine.
adj
(mathematics) Having the form of a cosine
adj
(mathematics) Symplectic and having a closed contact form as well.
n
(mathematics, uncommon) Synonym of hyperbolic cotangent.
n
(mathematics, informal) The space so mapped.
n
(mathematics) The trigonometric function 1 − cos(x)
n
(trigonometry) The trigonometric function 1 − sin(x).
n
(trigonometry) coversed sine
n
(graph theory) A 3-regular graph with 28 vertices and 42 edges, one of the 13 known cubic distance-regular graphs.
n
(geometry, algebra) A graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
n
(mathematics) The third power of a number, value, term or expression.
n
(mathematics) Of a number or expression, a number or expression the cube of which is equal to the given number or expression.
adj
(algebraic geometry) Of a class of polynomial of the form ax³+bx²+cx+d
n
(mathematics) A plane curve having the equation y=a.x³+b.x²+c.x+d.
n
(mathematics) A polynomial equation whose greatest exponent is 3.
n
(graph theory) A 3-regular graph; i.e., a graph whose every vertex has degree three.
n
(mathematics) an invariant of a cubic form
adj
(geometry, of a transformation) Being a Cremona transformation such that the homaloids of the transformation and its inverse all have degree 3.
adj
(mathematics) Of or pertaining to the inverse trigonometric functions: arcsine, arccosine, arctangent, arccotangent, arcsecant, and arccosecant.
adj
(mathematics) of, or relating to the complex roots of unity
n
A kind of fractal curve.
n
(geometry) The codimension of a linear system in the corresponding complete linear system.
n
(mathematics) A conic section that is reducible as the union of two lines.
n
(mathematics) The number of possible paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (m, n), using only single steps north, northeast, or east.
n
A pair of antiparallel edges in a directed graph.
n
(mathematical analysis) a metric d such that for any pair of points x and y, d(x,y)=0 if x=y and d(x,y)=1 if x ne y.
adj
(mathematics, rare, of a polyomino) That has two neighbouring squares cut away diagonally.
n
The topological space obtained by identifying the sides comprising the boundary of a triangle, two sides with consistent orientation and the third with the reverse orientation.
n
(mathematics, combinatorics) A string consisting of n X's and n Y's such that no initial segment of the string has more Y's than X's.
n
(mathematics) The ratio, constant for any particular conic section, of the distance of a point from the focus to its distance from the directrix.
n
(mathematics) Any of a family of elliptic curves with applications in cryptography.
adj
(mathematics) Of or pertaining to an ellipsoid.
adj
(mathematics, in combination, of certain functions, equations and operators) That has coefficients satisfying a condition analogous to the condition for the general equation for a conic section to be of an ellipse.
n
(algebraic geometry) The algebraic set of an equation which equates the square of one variable to a reduced cubic polynomial in another variable, over some field, and such that the discriminant of the reduced cubic is non-zero.
n
(mathematical analysis) Any of a particular class of second-order linear differential operators.
adj
(mathematics, rare) Elliptic.
n
(countable, mathematics) A measure of this flattening that is a function of the ellipse's equatorial and polar radii
adj
Archaic spelling of elliptic. [(geometry) Of or pertaining to an ellipse.]
n
(mathematics, physics) A type of conifold ring proposed in some forms of supersymmetry
n
(geometry) A mathematical curve, surface, or higher-dimensional object that is the tangent to a given family of lines, curves, surfaces, or higher-dimensional objects.
adj
(geometry) Being an affine transformation that preserves area.
adj
(mathematics, of a map) In which each face has the same number of edges
adj
(geometry) Such that each complementary region is irreducible, the boundary of each complementary region is incompressible by disks and monogons in the complementary region, and no leaf is a sphere or a torus bounding a solid torus in the manifold.
adj
(geometry) Adhering to the principles of traditional geometry, in which parallel lines are equidistant.
n
(geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (aₓ, a_y) and b = (bₓ, b_y) is defined as:
n
(geometry) The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line.
n
(mathematics) Two-dimensional Euclidean space.
n
(differential geometry) Formula which calculates the normal curvature of an arbitrary direction in the tangent plane in terms of the principal curvatures 𝜅₁ and 𝜅₂ and the angle 𝜃 which that direction makes with the first principal direction:
n
(trigonometry) The trigonometric function csc(x) − 1. Abbreviation: excsc
n
(trigonometry) The trigonometric function sec(x) − 1. Abbreviation: exsec
n
(finite geometry) The finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point.
n
(mathematics) The algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation.
n
(geometry, uncountable) The branch of geometry that concerns geometric systems with only a finite number of points.
n
(mathematics) The elliptic curve associated with a solution of Fermat's equation.
n
(mathematics) An equivalence class of parametrized surfaces in a metric space.
n
(mathematics) Any metric space whose elements are functions
n
(vector calculus) a surface that Gauss' law is applied to
n
(mathematics, sciences) A course allowing the parallel-transport of vectors along a course that causes tangent vectors to remain tangent vectors throughout that course (a straight curve, a line that is straight).
n
(mathematics) The characterisation of a differentiable manifold in terms of its geodesics, such as the quality of a submanifold being totally geodesic.
n
(algebraic geometry, countable) A mathematical object comprising representations of a space and of its spatial relationships.
n
(mathematics) In dynamical systems theory, a chaotic two-dimensional map given by the piecewise linear transformation x_n+1=1-y_n+|x_n|\y_n+1=x_n.
n
(topology) A connection between the edges of two planes, or between the points at the ends of two lines.
adj
(mathematics, quantum mechanics) of or pertaining to the generalization of the Feynman path integral to an integral over random surfaces
n
(geometry) Short for Gougu theorem, a term for the Pythagorean theorem. [(geometry) Pythagorean theorem]
n
(geometry) Pythagorean theorem
n
(geometry) Pythagorean theorem
adj
(mathematics) Of or relating to groupoids.
n
(trigonometry) Abbreviation of hacoversed sine. [(trigonometry) The trigonometric function equal to half the coversed sine. Abbreviation: hacoversin]
n
(trigonometry) the hacoversed sine
n
(mathematical analysis) A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero.
n
(trigonometry) the trigonometric function (1 + cos(x)) / 2, equal to half the vercosine
n
(trigonometry, rare) The trigonometric function defined as half the versed sine. Abbreviation: haversin
n
(trigonometry) Abbreviation of haversine. [(trigonometry) The haversed sine.]
n
(trigonometry) The haversed sine.
n
(differential geometry) A type of plane curve; see Hedgehog (geometry).
n
A kind of transformation in three-dimensional space, frequently used in geodesy to avoid distortion when converting from one datum to another.
adj
(mathematics) Describing a path between two points of equilibrium
n
(mathematics) The arithmetic operation of repeated pentation.
n
A treelike data structure each of whose nodes has up to sixteen children. It can be used to partition a four-dimensional space by recursively subdividing it.
n
(geometry) A continuous fractal space-filling curve.
adj
(mathematics) Including every edge exactly once and where, for all x and y, the edges (x,y) and (y,x) have opposite parities.
n
(differential geometry) Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P.
n
(mathematics) A shell bounded by two similar ellipsoids having a constant ratio of axes http://mathworld.wolfram.com/Homeoid.html.
adj
(mathematics) Describing a path that starts and ends at the same point of equilibrium
n
(geometry) Any one of a set of n + 1 coordinates which non-uniquely identify a point in an n-dimensional projective space; when such coordinates are all multiplied by the same scalar, then the set of them still identifies the same point.
n
Obsolete form of homoeoid. [(mathematics) A boundlessly thin shell constrained by a couple of similar surfaces with nearly identical orientations.]
adj
(mathematics) Related to, or constructed from horicycles
n
(mathematics) Any of a class of chaotic maps of the square into itself, used in the study of dynamical systems.
n
(geometry) A compact Riemann surface with precisely 84(g − 1) automorphisms, where g is the genus of the surface. This number is maximal by virtue of Hurwitz's theorem on automorphisms.
n
(geometry) The set of all points that make a hypersphere.
n
(geometry) A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone. The function y(x) = 1/x draws a hyperbola.
n
(countable, obsolete) A hyperbola.
adj
(topology) Of, pertaining to, or in a hyperbolic space (a space having negative curvature or sectional curvature).
n
(mathematics) An angle that describes a position along a hyperbola.
n
(geometry) A type of geometry that rejects the parallel postulate. Given a straight line L and a point P not on the line, more than one straight line can be drawn through P without intersecting L.
n
(mathematics) A topological space homeomorphic to a plane (or open disk) and equipped with a hyperbolic metric.
n
(mathematics) An area on a plane bounded by two rays from the origin and a rectangular hyperbola.
n
(mathematics) A hyperbolic function that is the analogue of the sine function for hyperbolic spaces, taking in a hyperbolic angle as an argument and returning the y-coordinate for the corresponding point on the unit hyperbola. It is written in symbol sinh and can be represented as: sinh (x)= tfrac 1 2(eˣ-e⁻ˣ)
n
(mathematics) Any space exhibiting hyperbolic geometry rather than Cartesian geometry
adj
(mathematics) Having topological properties that are equivalent to the existence of a hyperbolic structure.
n
(countable, geometry) A blow-up of a curve at a point.
n
A particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign.
n
(computing) A computer architecture in which each processor is connected to n others, by analogy with a hypercube of n dimensions.
n
(geometry) A singularity of a curve of some multiplicity r whose tangent cone is a single line meeting the curve with order r+1.
n
(hyperbolic geometry) A curve whose points have the same orthogonal distance from a given straight line.
n
(geometry) Specifically, a superellipse with an exponent (shape parameter) greater than that of the ellipse (two).
n
(geometry) A figure, related to the hypersphere, having ellipsoidal rather than spherical symmetry
adj
(geometry) Relating to, or having the form of a hyperellipsoid
adj
(mathematics) Pertaining to a hyperellipse.
n
(mathematics) A hyperplane that forms a boundary of a polytope
n
(geometry) A point of a curve where the tangent line has contact of order at least 4.
n
(mathematics) A three-dimensional analog of a honeycomb structure
n
(physics) A state of many interconnected dimensions.
adj
Alternative form of hyperkähler [(geometry, of a manifold) Being a quaternionic analogue of a Kähler manifold.]
n
(mathematics) A particular set of points, related to an oval, in a projected plane
n
(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)
n
A higher-dimensional shape analogous to the three-dimensional pyramid.
n
(mathematics) A particular generalization of a superquadric
adj
(mathematics) Relating to a hyperradius
adj
(mathematics) That scales in a higher dimension
n
(mathematics) A kind of convex polytope that generalizes the simplex, defined as the convex hull of a d-dimensional vector whose coefficients consist of k ones and d−k zeros.
n
(mathematics) A Euclidian space of unspecified dimension.
n
(physics) A system of streamlines defined by the three principal eigenvectors of a symmetric second-order tensor
n
(mathematics) A four-dimensional equivalent of a torus
adj
(mathematics, of a virtual double category) Having additional cells with nullary target.
n
(geometry) A volume in more than three dimensions.
n
(geometry) A superellipse with an exponent (shape parameter) smaller than that of the ellipse, i.e. less than two.
n
(geometry) Absolute geometry, an axiomatised geometry in which the parallel postulate is absent and not replaced by an alternative, and of which Euclidean geometry and some non-Euclidean geometries are subtypes.
n
(differential calculus, differential geometry) A tangent to a curve at a point of inflection.
adj
Relating to the same ellipse, or the same elliptic function.
adj
(dated, mathematics) isosceles
n
(mathematics) An intersection of n hypersurfaces in an n-dimensional projective space
n
(mathematics) The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.
n
(mathematics) The lines of a 3-dimensional projective space, S, can be viewed as points of a 5-dimensional projective space, T. In that 5-space, the points that represent each line in S lie on a hyperbolic quadric, Q, known as the Klein quadric.
n
(trigonometry) A generalization of the Pythagorean theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.
n
(mathematics) The lemniscate of Bernoulli
n
(mathematics) Any closed curve described by a Cartesian equation of the form (x²+y²)²=2a²(x²-y²).
n
(mathematics) Synonym of Lissajous figure
n
(mathematics) A plane curve traced by a point which executes two perpendicular independent harmonic motions, the frequencies of which are in a simple ratio.
adj
Of or related to hyperbolic geometry, which was developed by Nikolai Lobachevsky.
n
(computer graphics) A polygon mesh representing the continuous, closed surface of a solid object
n
(mathematics) A mathematically representative object in a set of objects; it has the smallest average dissimilarity to all other objects in the set.
adj
(dated, geometry) non-Euclidean
adj
(mathematics) Describing a structure, on a smooth manifold, that consists of a pair of tensors: a skew-symmetric Poisson tensor and a symmetric metric tensor.
n
(mathematics, physics) A four-dimensional real vector space equipped with an inner product of signature (−,+,+,+) or (+,−,−,−), in which special relativity is formulated
n
(mathematics, relativity) A geometrically flat spacetime, i.e. one with zero curvature.
n
(geometry) A theorem stating that it is not possible to dissect a square into an odd number of triangles of equal area.
n
(number theory, recreational mathematics) A magic square of order n containing the numbers 1 to n² and where each 2 × 2 subsquare sums to 2s, where s = n² + 1, and all pairs of integers distant n/2 along a (major) diagonal sum to s.
adj
(mathematics) Pertaining to a generalization of a cosimplicial space to diagrams of spaces that are cosimplicial in each direction.
n
(mathematics) Either of the two parts of a double cone.
n
(geometry) A plane curve resembling two intersecting ellipses
n
(geometry) Synonym of kissing number
n
Synonym of Newton-Cotes formula
n
(geometry) Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience.
adj
(geometry, uncommon) Self-intersecting.
adj
(geometry) Being or relating to the theorem in symplectic geometry stating that one cannot embed a sphere into a cylinder via a symplectic map unless the radius of the sphere is less than or equal to the radius of the cylinder.
n
Abbreviation of normal. [(geometry) A line or vector that is perpendicular to another line, surface, or plane.]
n
Any force acting normal, to a surface, or perpendicular to the tangent plane.
n
In a closed space-time, especially for an Einstein cylinder, null infinity for a given point is the limit of convergence of the light cone most distant from the given point. That is, it is the limit of a set of points that each have a time-like separation from every point that has a space-like separation from the given point.
n
(mathematics) A rectangle in the real plane which is an open set: i.e., which does not contain its edges. If the sides of the open rectangle are parallel to the plane's axes, then the open rectangle can be described as the Cartesian product of two open intervals.
n
(mathematical analysis, differential geometry, countable) The choice of which ordered bases are "positively" oriented and which are "negatively" oriented on a real vector space.
adj
(mathematics) Converted into an orientifold
n
(mathematics) A bicupola in which the bases have the same orientation
n
(mathematics) In a projective plane, a set of points such that no three are collinear and there is a unique tangent line at each point.
adj
(graph theory, of a graph) Containing cycless of every possible length (from 3 to the order of the graph).
adj
(mathematics) Of a magic square: having the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant.
n
(number theory, recreational mathematics) A magic square with the additional property that the broken diagonals also summate to the magic constant.
adj
(chiefly mathematics) Of, or pertaining to, or in the shape of a parabola or paraboloid.
adj
(geometry) Hyperbolic complex.
n
(geometry) A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side.
adj
(mathematics, of a matrix) In which the only nonzero entries are on the main diagonal, and the first two diagonals above and below it
adj
(mathematics) Of or relating to the fifth degree, such as a pentic polynomial
adj
(mathematics) Having the odd canonical form; special peculiar.
n
Synonym of split-complex number
n
Alternative spelling of pi-plus [The positive pion, composed of an up quark and an anti-down quark.]
n
(graph theory) A graph which can be embedded in a plane in such a way that its edges only intersect at vertices, i.e., they do not cross each other.
n
(graph theory) An embedding of a planar graph in a plane.
adj
(mathematics) closed in multiple ways
n
The theorem that the only simply connected, closed 3-dimensional manifold is a sphere.
n
(mathematics) The intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace (the Poincaré section), transversal to the flow of the system.
n
(rare, mathematics) polygon
n
(mathematics) Any pattern formed from a polyomino by removing half of each square such that the squares are still joined
n
(mathematics) A Cartesian product of discs.
n
(mathematics, computer graphics) A continuous line composed of one or more line segments.
n
(mathematics) A particular form of polytope
n
(mathematics) A connected graph.
n
(mathematics) A two-dimensional coloured image, prepared using polynomiography, that is the representation of a polynomial
adj
(mathematics) Multiply symplectic
adj
(mathematics) Of or pertaining to polytopes.
n
(mathematics) The set of all vectors of a given dimension such that each element of the vector is within a radius r of the corresponding element of a central vector.
n
(mathematics) A particular solution to an equation concerning self-gravitating, polytropic fluid
adj
(mathematics) Antisymmetric.
n
(mathematics) a branch of mathematics that investigates those properties of figures that are invariant when projected from a point to a line or plane
n
(geometry) A kind of geometrical space in which only relation(s) of incidence between points and lines matter; in such a space distances or angles do not matter and parallelism (as in an affine space) does not matter either.
n
(geometry) A theorem that states in a cyclic quadrilateral, the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the two pairs of opposite sides.
n
(trigonometry) The equality sin (x)²+ cos (x)²=1, holding for all real and complex x, equivalent to the application of the Pythagorean theorem to the unit circle.
n
(mathematics) A set of three positive integers a, b and c, for which a²+b²=c²
adj
(mathematics) of an equation, of the form ax²+bx+c=0.
n
(algebra) An expression consisting of four terms.
n
(mathematics, obsolete) The left hand side of a linear differential equation whose right hand side is zero.
n
(mathematics) A curve describing such an equation or function.
adj
(statistics) Describing an orthogonal rotation that maximizes the squared loadings for each variable rather than each factor.
n
(mathematics) A Jordan curve in the complex plane that is the image of a circle under a quasiconformal mapping of the plane onto itself.
adj
(mathematics) Having an approximate unit consisting of projections which is quasicentral.
n
The application of the mathematics of quaternions in various disciplines.
n
(mathematics) a quintic polynomial: ax⁵+bx⁴+cx³+dx²+ex+f
n
(computing theory) An algorithm that examines a curve composed of line segments (i.e. a polyline) and attempts to find a similar curve with fewer points.
n
(geometry) A three-dimensional vector space over the field of real numbers in which one-dimensional linear subspaces are considered as “points” and two-dimensional linear subspaces are considered as “lines”. Equivalently, a sphere in which pairs of antipodal points are considered as “points” and great circles are considered as “lines”.
n
(mathematics) A hyperbola where the two asymptotes intersect at a right angle.
adj
(mathematics, sciences) Pertaining to the two-dimensional modelling of three-dimensional stress paths that are symmetric about an axis.
adj
(mathematics) Of a cusp: defined by the equation (y-x²)²=x⁵, which is parametrized by (t²,t⁴+t⁵); having two branches with concavity in the same direction.
n
(mathematics, geometry) An operation on a metric space that is a continuous isometry and fixes at least one point.
n
(mathematics, engineering) The complex plane on which Laplace transforms are graphed; a mathematical domain where processes are viewed in the frequency domain rather than the time domain; used as a graphical analysis tool in engineering and physics.
n
(trigonometry) In a right triangle, the reciprocal of the cosine of an angle. Symbol: sec
n
(mathematics) An iterative numerical method for finding a root of an equation f(x)=0, using a succession of roots of secant lines to better approximate the root.
n
(geometry) One branch of a parabola, terminating at the principal vertex of the curve.
n
(geometry, differential geometry) The differential of the Gauss map of an oriented surface at a given point on the surface.
n
(mathematics) An extension of the wavelet, allowing the efficient encoding of anisotropic features in multivariate problem classes.
n
(mathematics) A plane fractal, a generalization of the Cantor set to two dimensions, formed by repeated subdivision of a square.
n
(mathematics) Any of a recursively defined sequence of continuous closed plane fractal curves which, in the limit n→∞, completely fill the unit square.
n
(trigonometry) law of sines
n
(trigonometry) law of sines
n
(trigonometry) The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.
n
(trigonometry) law of sines
n
(trigonometry, signal processing) A periodically oscillating waveform as described by the sine function, possibly multiplied by some amplitude, shifted by some phase, and translated by an additive constant.
n
(trigonometry) Synonym of sine.
adj
(mathematics) sinusoidal.
adj
(mathematics) symplectic in a more generalised manner
n
(mathematics) A field of plotted slopes of a differentiable function.
n
(countable, mathematics) A generalized construct or set whose members have some property in common; typically there will be a geometric metaphor allowing these members to be viewed as "points". Often used with a restricting modifier describing the members (e.g. vector space), or indicating the inventor of the construct (e.g. Hilbert space).
n
(mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)
n
Alternative form of space-filling curve [(mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)]
n
(mathematics) The solutions to Laplace's equation using spherical coordinates
n
(mathematics, computing) Any of a number of smooth curves used to join points.
adj
(mathematics) Permitting a grouping of 2-cells in oppositely oriented identifiable pairs.
adj
Of a Hermitian matrix, having real non-positive off-diagonal elements. These matrices have elements of quantum mechanics and classical theory of stochastic matrices. For non-technical purposes ‘stoquastic’ is equivalent to “avoiding the sign problem”.
n
(mathematics) A plane making up part of another plane.
n
(geometry) A polyhedron at the intersection of simplexes.
adj
(geometry) Relating to, or composed of subsimplexes
n
(algebra, geometry) a geometric surface constituting a transition between a cube (or similar surface) and a catenoid.
adj
(mathematics) Describing any of several extensions of conic curves and equations
n
(geometry) A closed curve, of form y = (1-xⁿ)^(1/n) (where n > 2), having properties intermediate between those of a circle and a square
n
(algebra, geometry) a geometric shape constituting a transition between a rectangle and a circle; a closed curve, of which the circle and ellipse are special cases, whose parametric equation is x = a.cos^(2/r)t, y = b.cos^(2/r)t
adj
Relating to a superellipse.
adj
Having the shape of a superellipse.
n
(physics) A Feynman diagram that calculates scattering amplitudes in a supersymmetric theory using the advantages of the superspace formalism.
n
(mathematics) hyperplane
n
(geometry) Any closed curve that is a generalization of a superellipse; it is defined by a superformula
adj
(mathematics) Describing a certain class of elliptic curves
adj
(mathematics, of a knot) Having the property of being a superslice.
n
(mathematics) An analogue in a space of four or more dimensions of a solid in three dimensions.
n
(mathematics) Any of several surfaces related mathematically to a torus
n
(mathematics) supertoroid
n
(mathematics, physics) A supersymmetric extension of twistors, having n degrees of freedom (where n is the number of supersymmetries) in addition to those of a standard twistor.
n
(mathematics) A symplectic bilinear form, manifold, geometry, etc.
adj
(mathematics) of a surface whose Gaussian curvature is positive at all points
adj
(mathematics) flat, of finite representation, and locally a complete intersection.
n
(geometry) A point of a curve where two or more osculating circles to the curve at that point are tangent, so that two branches of the curve have ordinary tangency at the double point.
n
(mathematics) A function of an angle that gives the ratio of the sine to the cosine, in either the real or complex numbers. Symbols: tan, tg.
n
(differential geometry) Synonym of tangent (“straight line touching a curve at a single point without crossing it there”).
n
(differential geometry) Given a point P on a surface M, the tangent plane of M at point P, denoted by T_P(M), is the plane passing through P which contains the tangent lines of all the curves on M passing through P.
n
(mathematics) A graph of the tan (tangent) function
n
(mathematics) A curve, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall.
n
Alternative form of Chebyshev distance [(mathematics) A metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension.]
n
(mathematics, obsolete) A norm operation on the quaternion algebra.
n
(mathematics) A vector space whose basis of real numbers has three vectors
n
(mathematics) A generalization of certain properties of multidimensional spaces.
adj
(mathematics) describing a submanifold whose geodesics are also geodesics of the surrounding manifold
n
(mathematics) A group that can be realized geometrically by sequences of reflections across the sides of a triangle.
adj
(graph theory) Of an undirected graph in which no three vertices form a triangle of edges.
n
(mathematics) The equivalent of a complex number in three dimensions
adj
(graph theory) Of a connected graph: needing three vertices removed for it to become disconnected.
n
(uncountable) Trigonometry.
n
(mathematics) Either of a pair of trigonometric functions that have equal values when their arguments are complementary angles, e.g. sine and cosine.
n
(trigonometry) Any function of an angle expressible as the ratio of two of the sides of a right triangle that has that angle (e.g., sine), or that subtracts 1 from such a ratio or subtracts such a ratio from 1 (e.g., coversed sine).
n
A tangent space meeting a quartic surface in a conic.
adj
(mathematics) Pertaining to tropical geometry.
n
(mathematics) A recent branch of geometry that can be described as a piecewise linear version of real algebraic geometry.
n
(geometry, topology, mathematical analysis) A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point.
adj
(mathematics) Being or relating to a kind of hyperelliptic line integral involving a polynomial of degree 5 or 6.
adj
(mathematics) Related to or involving a Gegenbauer polynomial.
n
(mathematics) A set of points on a plane whose distance from a given point is less than or equal to one.
n
(geometry) The hyperbola that satisfies the equation: x²-y²=1
n
(trigonometry) The trigonometric function 1 − cos(x).
n
(trigonometry) The versed sine.
n
(mathematics) A diagram that assigns a set of points in a plane to an equal number of cells, such that each point p is inside a cell consisting of all regions closer to p than to any other point.
n
(differential geometry) A measure of the curvature of spacetime (or, more generally, a pseudo-Riemannian manifold), differing from the Riemann tensor in that it does not convey information on how the volume of the body changes, but only how its shape is distorted by the tidal force.
n
(mathematics) A method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable.
adj
(of a topological space) In which every geodesic triangle satisfies that every point on the triangle is within a distance of δ (some constant) of each side of the triangle.
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