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Geomview
The Geometry Center was a mathematics research and education center at the University of Minnesota. It was established by the National Science Foundation in the late 1980s and closed in 1998. The focus of the center's work was the use of computer graphics and visualization for research and education in pure mathematics and geometry. The center's founding director was Al Marden. Richard McGehee directed the center during its final years. The center's governing board was chaired by David P. Dobkin. Geomview Much of the work done at the center was for the development of Geomview, a three-dimensional interactive geometry program. This focused on mathematical visualization with options to allow hyperbolic space to be visualised. It was originally written for Silicon Graphics workstations, and has been ported to run on Linux systems; it is available for installation in most Linux distributions through the package management system. ''Geomview'' can run under Windows using Cygwin and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interactive Geometry Software
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines, circles or other points. After some construction is done, one can move the points one started with and see how the construction changes. History The earliest IGS was the Geometric Supposer, which was developed in the early 1980s. This was soon followed by Cabri in 1986 and The Geometer's Sketchpad. Comparison There are three main types of computer environments for studying school geometry: supposers, dynamic geometry environments (DGEs) and Logo-based programs. Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions. The main example of a supposer is the Geometric Supposer, which does not have draggable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linux Journal
''Linux Journal'' (''LJ'') is an American monthly technology magazine originally published by Specialized System Consultants, Inc. (SSC) in Seattle, Washington since 1994. In December 2006 the publisher changed to Belltown Media, Inc. in Houston, Texas. Since 2017, the publisher was Linux Journal, LLC. located in Denver, Colorado. The magazine focused specifically on Linux, allowing the content to be a highly specialized source of information for open source enthusiasts. The magazine was published from March 1994 to August 2019, over 25 years, before being bought by Slashdot Media in 2020. History ''Linux Journal'' was the first magazine to be published about the Linux kernel and operating systems based on it. It was established in 1994. The first issue was published in March 1994 by Phil Hughes and Bob Young, who later co-founded Red Hat, and it featured an interview with Linux creator Linus Torvalds. The publication's last print edition was August 2011, issue 208. Beginning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic 3-manifold
In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1. It is generally required that this metric be also complete: in this case the manifold can be realised as a quotient of the 3-dimensional hyperbolic space by a discrete group of isometries (a Kleinian group). Hyperbolic 3–manifolds of finite volume have a particular importance in 3–dimensional topology as follows from Thurston's geometrisation conjecture proved by Perelman. The study of Kleinian groups is also an important topic in geometric group theory. Importance in topology Hyperbolic geometry is the most rich and least understood of the eight geometries in dimension 3 (for example, for all other geometries it is not hard to give an explicit enumeration of the finite-volume manifolds with this geometry, while this is far f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SnapPea
SnapPea is free software designed to help mathematicians, in particular low-dimensional topologists, study hyperbolic 3-manifolds. The primary developer is Jeffrey Weeks, who created the first version as part of his doctoral thesis, supervised by William Thurston. It is not to be confused with the unrelated android malware with the same name. The latest version is 3.0d3. Marc Culler, Nathan Dunfield and collaborators have extended the SnapPea kernel and written Python extension modules which allow the kernel to be used in a Python program or in the interpreter. They also provide a graphical user interface written in Python which runs under most operating systems (see external links below). The following people are credited in SnapPea 2.5.3's list of acknowledgments: Colin Adams, Bill Arveson, Pat Callahan, Joe Christy, Dave Gabai, Charlie Gunn, Martin Hildebrand, Craig Hodgson, Diane Hoffoss, A. C. Manoharan, Al Marden, Dick McGehee, Rob Meyerhoff, Lee Mosher, Wal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Surface
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. Definitions Minimal surfaces can be defined in several equivalent ways in R3. The fact that they are equivalent serves to demonstrate how minimal surface theory lies at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Evolver
Surface Evolver is an interactive program for the study of surfaces shaped by surface tension and other energies, and subject to various constraints. A surface is implemented as a simplicial complex. The user defines an initial surface in a datafile. The Evolver evolves the surface toward minimal energy by a gradient descent method. The aim can be to find a minimal energy surface, or to model the process of evolution by mean curvature. The energy in the Evolver can be a combination of surface tension, gravitational energy, squared mean curvature, user-defined surface integrals, or knot energies. The Evolver can handle arbitrary topology, volume constraints, boundary constraints, boundary contact angles, prescribed mean curvature, crystalline integrands, gravity, and constraints expressed as surface integrals. The surface can be in an ambient space of arbitrary dimension, which can have a Riemannian metric, and the ambient space can be a quotient space under a group action. Evo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satellite Constellation
A satellite constellation is a group of artificial satellites working together as a system. Unlike a single satellite, a constellation can provide permanent global or near-global coverage, such that at any time everywhere on Earth at least one satellite is visible. Satellites are typically placed in sets of complementary orbital planes and connect to globally distributed ground stations. They may also use inter-satellite communication. Other satellite groups Satellite constellations should not be confused with: * ''satellite clusters'', which are groups of satellites moving very close together in almost identical orbits (see satellite formation flying); * '' satellite series'' or ''satellite programs'' (such as Landsat), which are generations of satellites launched in succession; * ''satellite fleets'', which are groups of satellites from the same manufacturer or operator that function independently from each other (not as a system). Overview Satellites in Medium Earth orbi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar System" and "solar system" structures in theinaming guidelines document. The name is commonly rendered in lower case ('solar system'), as, for example, in the ''Oxford English Dictionary'' an''Merriam-Webster's 11th Collegiate Dictionary''. is the gravity, gravitationally bound system of the Sun and the objects that orbit it. It Formation and evolution of the Solar System, formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud. The solar mass, vast majority (99.86%) of the system's mass is in the Sun, with most of the Jupiter mass, remaining mass contained in the planet Jupiter. The four inner Solar System, inner system planets—Mercury (planet), Mercury, Venus, Earth and Mars—are terrest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Group
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object ''X'' is ''G'' = Sym(''X''). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure. Introduction We consider the "objects" possessing symmetry to be geometric figures, images, and patterns, such as a wallpaper pattern. For symmetry of physical objects, one may also take their physical composition as part of the pattern. (A pattern may be specified formally as a scalar field, a funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plug-in (computing)
In computing, a plug-in (or plugin, add-in, addin, add-on, or addon) is a software component that adds a specific feature to an existing computer program. When a program supports plug-ins, it enables customization. A theme or skin is a preset package containing additional or changed graphical appearance details, achieved by the use of a graphical user interface (GUI) that can be applied to specific software and websites to suit the purpose, topic, or tastes of different users to customize the look and feel of a piece of computer software or an operating system front-end GUI (and window managers). Purpose and examples Applications may support plug-ins to: * enable third-party developers to extend an application * support easily adding new features * reduce the size of an application by not loading unused features * separate source code from an application because of incompatible software licenses. Types of applications and why they use plug-ins: * Digital audio workstation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Web Browser
A web browser is application software for accessing websites. When a user requests a web page from a particular website, the browser retrieves its files from a web server and then displays the page on the user's screen. Browsers are used on a range of devices, including desktops, laptops, tablets, and smartphones. In 2020, an estimated 4.9 billion people used a browser. The most used browser is Google Chrome, with a 65% global market share on all devices, followed by Safari with 18%. A web browser is not the same thing as a search engine, though the two are often confused. A search engine is a website that provides links to other websites. However, to connect to a website's server and display its web pages, a user must have a web browser installed. In some technical contexts, browsers are referred to as user agents. Function The purpose of a web browser is to fetch content from the World Wide Web or from local storage and display it on a user's device. This process ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
