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Triangulation is a tactic used in chess to put one's opponent in zugzwang (a position in which it is a disadvantage to move). Triangulation is also called losing a tempo or losing a move .
Catalan's trapezoids are a countable set of number trapezoids which generalize Catalan’s triangle. Catalan's trapezoid of order m = 1, 2, 3, ... is a number trapezoid whose entries (,) give the number of strings consisting of n X-s and k Y-s such that in every initial segment of the string the number of Y-s does not exceed the number of X-s by m or more. [6]
This proof uses the triangulation definition of Catalan numbers to establish a relation between C n and C n+1. Given a polygon P with n + 2 sides and a triangulation, mark one of its sides as the base, and also orient one of its 2n + 1 total edges. There are (4n + 2)C n such marked triangulations for a given base.
Priyome – typical maneuver or technique in chess. Ply – half-turn, that is, one player's portion of a turn. Tempo – a "unit" similar to time, equal to one chess move, e.g. to lose a tempo is to waste a move or give the opponent the opportunity of an extra move. Sometimes a player may want to lose a tempo.
The cost of a single triangle in terms of the number of multiplications needed is the product of its vertices. The total cost of a particular triangulation of the polygon is the sum of the costs of all its triangles: (AB)C: (10×30×5) + (10×5×60) = 1500 + 3000 = 4500 multiplications
Triangulation (geometry), division of the Euclidean plane into triangles and of Euclidean spaces into simplices; Triangulation (topology), generalizations to topological spaces other than R d; Point-set triangulation, division of the convex hull of a point set into triangles using only that set as triangle vertices
A triangulation of the square that respects the gluings, like that shown below, also defines a triangulation of the torus. A two dimensional torus, represented as the gluing of a square via the map g, identifying its opposite sites; The projective plane admits a triangulation (see CW-complexes)
Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and, in the military, the gun direction, the trajectory and distribution of fire power of weapons. The use of triangles to estimate distances dates to antiquity.