Concepts inMöbius voting for surface correspondence
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R ¿ for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
more from Wikipedia
Isometry
For the mechanical engineering and architecture usage, see isometric projection. For isometry in differential geometry, see isometry (Riemannian geometry). In mathematics, an isometry is a distance-preserving map between metric spaces. Geometric figures which can be related by an isometry are called congruent. Isometries are often used in constructions where one space is embedded in another space.
more from Wikipedia
Proximity problems
Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects. A subset of these problems stated in terms of points only are sometimes referred to as closest point problems, although the term "closest point problem" is also used synonymously to the nearest neighbor search.
more from Wikipedia
Permutation matrix
In mathematics, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry 1 in each row and each column and 0s elsewhere. Each such matrix represents a specific permutation of m elements and, when used to multiply another matrix, can produce that permutation in the rows or columns of the other matrix.
more from Wikipedia
Codomain
In mathematics, the codomain or target set of a function is the set Y into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X ¿ Y. The codomain is also sometimes referred to as the range but that term is ambiguous as it may also refer to the image. The codomain is part of the modern definition of a function f as a triple (X, Y, F), with F a subset of the Cartesian product X × Y.
more from Wikipedia
Correspondence (mathematics)
In mathematics and mathematical economics, correspondence is a term with several related but not identical meanings. In general mathematics, a correspondence is an ordered triple (X,Y,R), where R is a relation from X to Y, i.e. any subset of the Cartesian product X×Y. In algebraic geometry, a correspondence between algebraic varieties V and W is in the same fashion a subset R of V×W, which is in addition required to be closed in the Zariski topology.
more from Wikipedia
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis. The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors.
more from Wikipedia
Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point (zero-dimensions), a line (one-dimension) and a space (three-dimensions). Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.
more from Wikipedia