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In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle.
A disk is said to be closed or open according to whether or not it contains the circle that constitutes its boundary. In Cartesian coordinates, the open disk of center Failed to parse (Missing texvc executable; please see math/README to configure.): (a, b)
and radius R is given by the formula
- Failed to parse (Missing texvc executable; please see math/README to configure.): D=\{(x, y)\in {\mathbb R^2}: (x-a)^2+(y-b)^2 < R^2\}
while the closed disk of the same center and radius is given by
- Failed to parse (Missing texvc executable; please see math/README to configure.): \overline{ D }=\{(x, y)\in {\mathbb R^2}: (x-a)^2+(y-b)^2 \le R^2\}.
The area of a closed or open disk of radius R is πR2 (see π).
The ball is the disk generalised to metric spaces. In context, the term ball may be used instead of disk.
In theoretical physics a disk is a rigid body which is capable of participating in collisions in a two-dimensional gas. Usually the disk is considered rigid so that collisions are deemed elastic.
Geometry [link]
The Euclidean disk is circular symmetrical.
Topological notions [link]
The open disk and the closed disk are not homeomorphic, since the latter is compact and the former is not. However from the viewpoint of algebraic topology they share many properties: both of them are contractible and so are homotopy equivalent to a single point. This implies that their fundamental groups are trivial, and all homology groups are trivial except the 0th one, which is isomorphic to Z. The Euler characteristic of a point (and therefore also that of a closed or open disk) is 1.
Every continuous map from the closed disk to itself has at least one fixed point (we don't require the map to be bijective or even surjective); this is the case n=2 of the Brouwer fixed point theorem. The statement is false for the open disk: consider for example
- Failed to parse (Missing texvc executable; please see math/README to configure.): f(x,y)=\left(\frac{x+\sqrt{1-y^2}}{2},y\right)
which maps every point of the open unit disk to another point of the open unit disk slightly to the right of the given one.
See also [link]
- Unit disk, a disk with radius one
- Annulus (mathematics)
- Ball (mathematics), the usual term for the 3-dimensional disk
- Disk algebra
- Lentoid
- Moment of inertia of a uniform disc
https://wn.com/Disk_(mathematics)
Tron (franchise)
Tron is an American science fiction media franchise. It began in 1982 with the Walt Disney Pictures film Tron. It was followed by various film tie-ins, a comic series and the 2010 sequel Tron: Legacy. More sequels were planned but have now been suspended, and a television series premiered on Disney XD in June 2012.
TRON also existed as the TRON command in the early versions of the computer programming language BASIC. TRON stood for TRace ON, which prompted the program to print or display line numbers for each command line of a program as it ran, in order to assist in the debugging of the program. In the TRON film, TRON became a character who worked in programs to defeat evil elements trying to subvert the program.
Films
Tron
Tron is a 1982 American action science fiction film by Walt Disney Pictures. It stars Jeff Bridges as Kevin Flynn, Bruce Boxleitner as Tron and his User Alan Bradley, Cindy Morgan as Yori and Dr. Lora Baines, and Dan Shor as Ram. David Warner plays all three main antagonists: the program Sark, his User Ed Dillinger, and the voice of the Master Control Program. It was written and directed by Steven Lisberger. Tron has a distinctive visual style, as it was one of the first films from a major studio to use computer graphics extensively.
List of Tron characters
This article covers notable characters of Tron franchise, including all of its various cinematic, literary, video game adaptations and sequels.
Development
For the first film, Richard Rickitt explains that to "produce the characters who inhabit the computer world, actors were dressed in costumes that were covered in black-and-white computer circuitry designs....With coloured light shining through the white areas of their costumes, the resulting characters appeared to glow as if lit from within....optical processes were used to create all of the film's computerized characters..." Frederick S. Clarke reports that "Tron: Legacy will combine live action with CGI," adding that "several characters...will be completely digital..."
Tron
Kevin Flynn
Kevin Flynn is a former employee at the fictional software company ENCOM and the protagonist of the first film. He is played by Jeff Bridges.
At the start of the first film, he is manager of "Flynn's", a video arcade where he impresses his patrons with his skills at games that (unknown to them) he designed at ENCOM, but remains determined to find evidence that CEO Ed Dillinger plagiarised Flynn's work to advance his position within the company. Throughout most of the film, Flynn travels around the digital world, accompanying the eponymous character Tron; but later discovers that as a User, he commands the physical laws of the digital world, enabling him beyond the abilities of an ordinary program. Eventually, he enables Tron to destroy the Master Control Program shown to oppress the digital world, and upon return to the material world obtains the evidence necessary to expose Dillinger, and becomes ENCOM's CEO himself.
Tron 2.0
Tron 2.0 is a first-person shooter computer game developed by Monolith Productions. According to Tron creator Steven Lisberger, Tron 2.0 was the official sequel to the 1982 film Tron, but was later declared non-canon by Tron: Legacy director Joseph Kosinski. The PC version of the game was released by Buena Vista Games on August 26, 2003. The Mac version was released by MacPlay on April 21, 2004.
Bruce Boxleitner reprises his role from the original film as Alan Bradley. Cindy Morgan, who also starred in the original film, voices a new character Ma3a, although Lora Bradley (now Alan's wife, deceased by the game's timeframe) is mentioned by name. Rebecca Romijn provides the voice of Mercury. A new 'light cycle' design was contributed to the game by Syd Mead. The game explained the Tron arcade game, which appears in-game, and film as based on Kevin Flynn's experiences inside ENCOM in the original film.
Plot
The story is centered around Alan's son Jethro ("Jet") Bradley. Since the film's events, ENCOM has been taken over by a company called Future Control Industries (fCon). After talking with his father who is kidnapped while on the phone with Jet, Jet is digitized by Ma3a, Alan's AI computer system, to aid her against Thorne, an executive from fCon improperly digitized into the computer who is now a virus throughout the system. Jet is mistakenly identified as the source of the corruption and captured by Kernel, the systems security control program.
Space (Modern Jazz Quartet album)
Space is an album by American jazz group the Modern Jazz Quartet featuring performances recorded in 1969 and released on the Apple label.
Reception
The Allmusic review stated "Overall this is an average but worthy outing from a group whose excellence could always be taken for granted".
Track listing
All compositions by John Lewis, except where noted.
Personnel
References
Space (punctuation)
In writing, a space ( ) is a blank area devoid of content, serving to separate words, letters, numbers, and punctuation. Conventions for interword and intersentence spaces vary among languages, and in some cases the spacing rules are quite complex. In the classical period, Latin was written with interpuncts (centred dots) as word separators, but that practice was abandoned sometime around 200 CE in favour of scriptio continua, i.e., with the words running together without any word separators. In around 600–800 CE, blank spaces started being inserted between words in Latin, and that practice carried over to all languages using the Latin alphabet (including English and most other Western European languages).
In typesetting, spaces have historically been of multiple lengths with particular space-lengths being used for specific typographic purposes, such as separating words or separating sentences or separating punctuation from words. Following the invention of the typewriter and the subsequent overlap of designer style-preferences and computer-technology limitations, much of this reader-centric variation was lost in normal use.
Four-dimensional space
In mathematics, four-dimensional space ("4D") is a geometric space with four dimensions. It typically is more specifically four-dimensional Euclidean space, generalizing the rules of three-dimensional Euclidean space. It has been studied by mathematicians and philosophers for over two centuries, both for its own interest and for the insights it offered into mathematics and related fields.
Algebraically, it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.
In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions (see below for the definition of the Minkowski metric/pairing). Spacetime is not a Euclidean space.
