Definition & Betydelse | Engelska ordet TRIANGULATIONS

Definition av TRIANGULATIONS

1. böjningsform av triangulation

Exempel på hur man kan använda TRIANGULATIONS i en mening

• Pure simplicial complexes can be thought of as triangulations and provide a definition of polytopes.
• Lucknow, along with Agra and Varanasi, is in the Uttar Pradesh Heritage Arc, a chain of survey triangulations created by the Government of Uttar Pradesh to boost tourism in the state.
• There are exactly 68 10-bit binary numbers in which each bit has an adjacent bit with the same value, exactly 68 combinatorially distinct triangulations of a given triangle with four points interior to it, and exactly 68 intervals in the Tamari lattice describing the ways of parenthesizing five items.
• With a direct ratio to the length of a surveyor's chain and the sides of both an acre and a square (mile), they were common tools used by surveyors, if only to lay out a known plottable baseline in rough terrain thereafter serving as the reference line for instrumental (theodolite) triangulations.
• In the first two complements to Analysis Situs, Poincaré gave a new proof in terms of dual triangulations.
• In algebraic topology it is sometimes useful to replace the original spaces with simplicial complexes via triangulations: The substitution allows to assign combinatorial invariants as the Euler characteristic to the spaces.
• It was clearly true that Betti numbers were unchanged by subdividing the triangulation, and therefore it was clear that any two triangulations that shared a common subdivision had the same Betti numbers.
• The dual polyhedron of the triaugmented triangular prism is an associahedron, a polyhedron with four quadrilateral faces and six pentagons whose vertices represent the 14 triangulations of a regular hexagon.
• For instance, the triangulations of regular polygons (with size given by the number of sides of the polygon, and a fixed choice of polygon to triangulate for each size) and the set of unrooted binary plane trees (up to graph isomorphism, with a fixed ordering of the leaves, and with size given by the number of leaves) are both counted by the Catalan numbers, so they form isomorphic combinatorial classes.
• Although it is possible to transform any two triangulations of the same polygon into each other by flips that replace one diagonal at a time, determining whether one can do so using only a limited number of flips is NP-complete.
• Renate Loll: physicist who worked on loop quantum gravity and more recently helped develop the causal dynamical triangulations approach to quantum gravity.
• It is known that the full classification of 3-manifolds can be done algorithmically, in fact, it is known that deciding whether two closed, oriented 3-manifolds given by triangulations (simplicial complexes) are equivalent (homeomorphic) is elementary recursive.
• In more general topological spaces, triangulations of a space generally refer to simplicial complexes that are homeomorphic to the space.
• The Hauptvermutung of geometric topology is a now refuted conjecture asking whether any two triangulations of a triangulable space have subdivisions that are combinatorially equivalent, i.
• A comparison of the original field notes, transcript notes, plats and report of the examiner, shows that at the season of the year (from December 1, 1884, to January 3, 1885) when the deputy pretends to have made the surveys, the deep snows made the survey at that time impossible; that in the original notes (which are now in this office) much is omitted that is found in the transcripts and data supplied from memory, or rather made up; that disregarding clerical errors the transcripts are not in any sense copies of the original notes; that triangulations omitted in originals are audaciously given in detail in the transcripts, just as if they had really been made in the field, that the high speed, more than 6 miles per day, at which it is pretended the work was executed, surpasses belief when we take into consideration the nature of the ground, and bear in mind that the surveying was done during the shortest days of the year; that the deputy gives descriptions of erroneous bearing trees where no such trees, either as regards size or species, are to be found; that in the face of all the embarrassing conditions, big canyons, high and steep mountains, deep snow, impenetrable chaparral, precipices impossible to ascend or descend, the deputy with his two parties of four men each, frequently with the impassable San Joaquin river between them, pretends to have subdivided T8SR24E at the rate of more than 6 miles per day, and then accomplishes the feat of recording all this work in one field book.
• The Struve Geodetic Arc is a chain of survey triangulations stretching from Hammerfest in Norway to the Black Sea, through ten countries and over , which yielded the first accurate measurement of a meridian arc.
• The quadrilateral case follows from a simple extension of the Japanese theorem for cyclic quadrilaterals, which shows that a rectangle is formed by the two pairs of incenters corresponding to the two possible triangulations of the quadrilateral.
• It is also possible to define related flip graphs for partitions into quadrilaterals or pseudotriangles, and for higher-dimensional triangulations.
• Pitts relating strongly irreducible Heegaard splittings to minimal surfaces, joint work with William Jaco on special triangulations of 3-manifolds (namely 0-efficient and 1-efficient triangulations), and joint work with Martin Scharlemann on the Rubinstein–Scharlemann graphic.
• While any two triangulations of the same region must have the same numbers of edges and triangles, the same is not true of pseudotriangulations; for instance, if the region is itself an n-vertex polygonal pseudotriangle, then a pseudotriangulation of it may have as few as one pseudotriangle and n edges, or as many as n − 2 pseudotriangles and 2n − 3 edges.

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