Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with history stretching back to antiquity. An ancient precursor is the Sanskrit treatise Shulba Sutras , or "Rules of the Chord", that is a book of algorithms written in 800 BCE. The book prescribes step-by-step procedures for constructing geometric objects like altars using a peg and chord.
Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(n2) and O(n log n) may be the difference between days and seconds of computation.
Computational Geometry, also known as Computational Geometry: Theory and Applications, is a peer-reviewed mathematics journal for research in theoretical and applied computational geometry, its applications, techniques, and design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects, as well as fundamental problems in various areas of application of computational geometry: in computer graphics, pattern recognition, image processing, robotics, electronic design automation, CAD/CAM, and geographical information systems.
The journal was founded in 1991 by Jörg-Rüdiger Sack and Jorge Urrutia. It is indexed by Mathematical Reviews, Zentralblatt MATH, Science Citation Index, and Current Contents/Engineering, Computing and Technology.
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.
Geometry is an album by Brazilian jazz saxophonist Ivo Perelman featuring American pianist Borah Bergman, which was recorded in 1996 and released on the English Leo label.
In his review for AllMusic, Alex Henderson says that "this CD doesn't quite fall into the 'essential' category... Nonetheless, Geometry is an enjoyable release that Perelman's more-devoted followers will want."
The Penguin Guide to Jazz notes that "Bergman is wily enough to find ways of both supporting and undercutting the mighty sound of the tenor."
In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.
In geometric group theory, a geometry is any proper, geodesic metric space. An action of a finitely-generated group G on a geometry X is geometric if it satisfies the following conditions:
If a group G acts geometrically upon two geometries X and Y, then X and Y are quasi-isometric. Since any group acts geometrically on its own Cayley graph, any space on which G acts geometrically is quasi-isometric to the Cayley graph of G.
Cannon's conjecture states that any hyperbolic group with a 2-sphere at infinity acts geometrically on hyperbolic 3-space.