Mathematics and computer science

• Subdivisions of spaces into triangles or higher dimensional simplices:
  • triangulation (geometry), division of the Euclidean plane into triangles and of Euclidean spaces into simplices
  • polygon triangulation
    Polygon triangulation
    In computational geometry, polygon triangulation is the decomposition of a polygonal area P into a set of triangles, i.e., finding the set of triangles with pairwise non-intersecting interiors whose union is P....
    
    , division of a polygon into triangles
  • point set triangulation
    Point set triangulation
    A triangulation of a set of points P in the plane is a triangulation of the convex hull of P, with all points from P being among the vertices of the triangulation. Triangulations are special cases of planar straight-line graphs....
    
    , division of the convex hull of a point set into triangles using only that set as triangle vertices
  • triangulation (topology)
    Triangulation (topology)
    In mathematics, topology generalizes the notion of triangulation in a natural way as follows:A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h:K\to X....
    
    , generalizations to topological spaces other than R^d
• In graph theory:
  • Maximal planar graph
    Planar graph
    In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints...
    
    s are sometimes called triangulations, and a maximal planar supergraph of a graph G may be called a triangulation of G.
  • Chordal graph
    Chordal graph
    In the mathematical area of graph theory, a graph is chordal if each of its cycles of four or more nodes has a chord, which is an edge joining two nodes that are not adjacent in the cycle. An equivalent definition is that any chordless cycles have at most three nodes...
    
    s are sometimes called triangulated graphs. As in the planar case, if a graph G is a subgraph of a chordal graph H, H may be called a triangulation of G.
• A triangulated category
  Triangulated category
  A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t-category is a triangulated category with a t-structure.- History :The notion of a derived category...
  
   is a category defined by a set of axioms involving triangles of arrows.
• Triangulation (computer vision)
  Triangulation (computer vision)
  In computer vision triangulation refers to the process of determining a point in 3D space given its projections onto two, or more, images. In order to solve this problem it is necessary to know the parameters of the camera projection function from 3D to 2D for the cameras involved, in the simplest...
  
   is the computation of a 3D point given its projection onto two, or more, images.
• In linear algebra
  Linear algebra
  Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
  
  , triangulation is a process of finding an upper triangular matrix similar to given a matrix. See Schur triangulation.
• Mobile phone tracking
  Mobile phone tracking
  Mobile phone tracking refers to the attaining of the current position of a mobile phone, stationary or moving. Localization may occur either via multilateration of radio signals between radio towers of the network and the phone, or simply via GPS...
  
   uses triangulation, (actually, trilateration), to calculate the location of the handset.

Other fields

• Triangulation (actuary), a model that actuaries use to predict future costs of past and current claims obligations.
• Triangulation (chess)
  Triangulation (chess)
  Triangulation is a tactic used in chess to put one's opponent in zugzwang. That is, it gets to the same position with the other player to move, when it is a disadvantage for that player to move, e.g. he has to give up a blockade and let the other player penetrate his position...
  
  , a maneuver in which one player moves a piece (often a king) in a triangular pattern in order to force the opponent to make a weakening move
• Triangulation (psychology), situation in which one person interacts with another person via an intermediary third person.
• Triangulation (politics)
  Triangulation (politics)
  Triangulation is the name given to the act of a political candidate presenting his or her ideology as being "above" and "between" the "left" and "right" sides of a traditional democratic "political spectrum". It involves adopting for oneself some of the ideas of one's political opponent...
  
  , the act of a candidate presenting his or her ideology as "above and between" the left and right side of the political spectrum
• Triangulation (social science)
  Triangulation (social science)
  In the social sciences, triangulation is often used to indicate that more than two methods are used in a study with a view to double checking results. This is also called "cross examination"....
  
  , the use of multiple cross-checked sources and methodology