List of points
Encyclopedia
In mathematics
, the following appear:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the following appear:
- Accumulation point
- Adherent pointAdherent pointIn mathematics, an adherent point is a slight generalization of the idea of a limit point....
- Antipodal pointAntipodal pointIn mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it — so situated that a line drawn from the one to the other passes through the centre of the sphere and forms a true diameter....
- Apex (geometry)Apex (geometry)In geometry, an apex is the vertex which is in some sense the highest of the figure to which it belongs.*In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side....
- Associated point
- Base point
- Closed point
- Cluster point
- Condensation pointCondensation pointIn mathematics, a condensation point p of a subset S of a topological space, is any point p, such that every open neighborhood of p contains uncountably many points of S....
- Conjugate point
- Critical pointCritical pointCritical point may refer to:*Critical point *Critical point *Critical point *Construction point of a ski jumping hill-See also:*Brillouin zone*Percolation thresholds...
- Decimal point
- Divisor point
- Embedded point
- Extreme pointExtreme pointIn mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S...
- Fixed pointFixed point (mathematics)In mathematics, a fixed point of a function is a point that is mapped to itself by the function. A set of fixed points is sometimes called a fixed set...
- Focal pointFocus (optics)In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
- Geometric point
- Hyperbolic pointHyperbolic pointIn applied mathematics, a hyperbolic point in a system dx/dt = F of ordinary differential equations is a stationary point x0 such that the eigenvalues of the linearized system have non-zero real part.-See also:*Anticlastic...
- Ideal point
- Inflection pointInflection pointIn differential calculus, an inflection point, point of inflection, or inflection is a point on a curve at which the curvature or concavity changes sign. The curve changes from being concave upwards to concave downwards , or vice versa...
- Integral point
- Isolated pointIsolated pointIn topology, a branch of mathematics, a point x of a set S is called an isolated point of S, if there exists a neighborhood of x not containing other points of S.In particular, in a Euclidean space ,...
- Generic pointGeneric pointIn mathematics, in the fields general topology and particularly of algebraic geometry, a generic point P of a topological space X is an algebraic way of capturing the notion of a generic property: a generic property is a property of the generic point.- Definition and motivation :A generic point of...
- Heegner pointHeegner pointIn mathematics, a Heegner point is a point on a modular elliptic curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class...
- Lattice hole, Lattice point
- Lebesgue point
- Limit pointLimit pointIn mathematics, a limit point of a set S in a topological space X is a point x in X that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself. Note that x does not have to be an element of S...
- MidpointMidpointThe midpoint is the middle point of a line segment. It is equidistant from both endpoints.-Formulas:...
- Nonsingular point
- Normal point
- Periodic pointPeriodic pointIn mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time.- Iterated functions :...
- Pinch pointPinch point (mathematics)right|frame|240px|Section of the [[Whitney umbrella]], an example of pinch point singularity.In geometry, a pinch point or cuspidal point is a type of singular point on an algebraic surface....
- Point (geometry)Point (geometry)In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
- Point sourcePoint sourceA point source is a localised, relatively small source of something.Point source may also refer to:*Point source , a localised source of pollution**Point source water pollution, water pollution with a localized source...
- Rational pointRational pointIn number theory, a K-rational point is a point on an algebraic variety where each coordinate of the point belongs to the field K. This means that, if the variety is given by a set of equationsthen the K-rational points are solutions ∈Kn of the equations...
- Recurrent pointRecurrent pointIn mathematics, a recurrent point for function f is a point that is in the limit set of the iterated function f. Any neighborhood containing the recurrent point will also contain iterates of it as well.-Definition:...
- Regular point, Regular singular point
- Saddle pointSaddle pointIn mathematics, a saddle point is a point in the domain of a function that is a stationary point but not a local extremum. The name derives from the fact that in two dimensions the surface resembles a saddle that curves up in one direction, and curves down in a different direction...
- Separable point
- Simple point
- Singular point of a curveSingular point of a curveIn geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on the type of curve being studied.-Algebraic curves in the plane:...
- Singular point of an algebraic varietySingular point of an algebraic varietyIn mathematics, a singular point of an algebraic variety V is a point P that is 'special' , in the geometric sense that V is not locally flat there. In the case of an algebraic curve, a plane curve that has a double point, such as the cubic curveexhibits at , cannot simply be parametrized near the...
- Smooth point
- Special point
- Stationary pointStationary pointIn mathematics, particularly in calculus, a stationary point is an input to a function where the derivative is zero : where the function "stops" increasing or decreasing ....
- Torsion point
- Vertex (curve)Vertex (curve)In the geometry of curves, a vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of curvature. Other special cases may occur, for instance when the second derivative is also zero, or when the curvature is constant...
, Vertex (geometry)Vertex (geometry)In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:... - Weierstrass pointWeierstrass pointIn mathematics, a Weierstrass point P on a nonsingular algebraic curve C defined over the complex numbers is a point such that there are extra functions on C, with their poles restricted to P only, than would be predicted by looking at the Riemann–Roch theorem...