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To use these invariants for the classification of topological spaces up to homeomorphism one needs invariance of the characteristics regarding homeomorphism. A famous approach to the question was at the beginning of the 20th century the attempt to show that any two triangulations of the same topological space admit a common subdivision.
In a network of fourteen cities a total of 53 triangulation measurements were made. In his calculations Snellius made use of a solution for what is now called the Snellius–Pothenot problem. Snellius' Triangulation (1615) By necessity Snellius's high points were nearly all church spires. There were hardly any other tall buildings at that time ...
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.
A shift or translation functor on a category D is an additive automorphism (or for some authors, an auto-equivalence) from D to D.It is common to write [] = for integers n.. A triangle (X, Y, Z, u, v, w) consists of three objects X, Y, and Z, together with morphisms :, : and : [].
The method of triangulation was first developed by Muslim mathematicians, who applied it to practical uses such as surveying [48] and Islamic geography, as described by Abu Rayhan Biruni in the early 11th century. Biruni himself introduced triangulation techniques to measure the size of the Earth and the distances between various places. [49]
Triangulation of Kodiak Island in Alaska in 1929. In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline by using trigonometry, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as ...
Head and cerebral structures (hidden) extracted from 150 MRI slices using marching cubes (about 150,000 triangles). Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, [1] for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels).
Edmund Gunter (1581 – 10 December 1626), was an English clergyman, mathematician, geometer and astronomer [1] of Welsh descent. He is best remembered for his mathematical contributions, which include the invention of the Gunter's chain, the Gunter's quadrant, and the Gunter's scale.