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# Topic: Dimension

###### In the News (Sun 11 Nov 18)

 Why Dell Dimensionâ„˘ Dimension is a balance of performance and value. Dimension desktops make it easier than ever for you to tap into the latest digital audio, video, photography and multimedia applications. Dimension desktops utilize the latest processor, chipset, memory, storage and graphics technologies, along with the latest versions of Microsoft Windows XP operating systems to deliver fast performance for all your small-business computing needs. www.dell.com /dimension   (371 words)

 Dimension - Wikipedia, the free encyclopedia In mathematics, dimensions are the parameters required to describe the position and relevant characteristics of any object within a conceptual space â€”where the dimensions of a space are the total number of different parameters used for all possible objects considered in the model. In the physical sciences and in engineering, the dimension of a physical quantity is the expression of the class of physical unit that such a quantity is measured against. The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that n+1-dimensional balls have n dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets. en.wikipedia.org /wiki/Dimension   (1640 words)

 Dimension (vector space) - Wikipedia, the free encyclopedia In mathematics, the dimension of a vector space V is the cardinality (i.e. Some simple formulae relate the dimension of a vector space with the cardinality of the base field and the cardinality of the space itself. The length of a module and the rank of an abelian group both have several properties similar to the dimension of vector spaces. en.wikipedia.org /wiki/Hamel_dimension   (501 words)

 [No title]   (Site not responding. Last check: ) Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space. Time is frequently referred to as the "fourth dimension"; time is not the fourth dimension of space, but rather of spacetime. The Krull dimension of a commutative ring is defined to be the maximal length of a strictly increasing chain of prime ideals in the ring. wikiwhat.com /encyclopedia/d/di/dimension.html   (579 words)

 PlanetMath: dimension The word dimension in mathematics has many definitions, but all of them are trying to quantify our intuition that, for example, a sheet of paper has somehow one less dimension than a stack of papers. One common way to define dimension is through some notion of a number of independent quantities needed to describe an element of an object. This is version 7 of dimension, born on 2003-10-18, modified 2004-03-29. planetmath.org /encyclopedia/Dimension3.html   (512 words)

 Fractal Dimension The dimension of the union of finitely many sets is the largest dimension of any one of them, so if we ``grow hair'' on a plane, the result is still a two-dimensional set. Not surprisingly, the box dimensions of ordinary Euclidean objects such as points, curves, surfaces, and solids coincide with their topological dimensions of 0, 1, 2, and 3-- this is, of course, what we would want to happen, and follows from the discussion at the beginning of §5.1. Thus, the embedding dimension of a plane is 2, the embedding dimension of a sphere is 3, and the embedding dimension of a klein bottle is 4, even though they all have (topological) dimension two. www.math.sunysb.edu /~scott/Book331/Fractal_Dimension.html   (1303 words)

 How many dimensions to our Universe? Of course not the three dimensions that we are used to, but some new dimensions of such a microscopic size that we would not be aware of their existence, unless we probed microphysics. Hence, a 5-dimensional field is identified in 4 dimensions to a tower of particles regularly spaced in mass-squared, the mass gap being given by the inverse of the compact dimension size. It is well-known in 4 dimensions that this constant is nothing but the vacuum energy: this is the source of the notorious cosmological problem: this vacuum energy is expected to be of the order of the fundamental scales in the microscopic theory, and this exceeds the observational constraint by many orders of magnitude. www.europhysicsnews.com /full/14/article5/article5.html   (2913 words)

 Fractal Curves and Dimension The topological dimension of a smooth curve is, as one would expect, one and that of a sphere is two which may seem very intuitive. To understand the notion of the similarity dimension, first observe that, if the initial line segment was 1 unit in length, then the second stage curve that consists of four segments each one third of the initial line, is 4/3 units in length. By one of Brouwer's theorems this function preserves the topological dimension of the segment (which is, of course 1). www.cut-the-knot.org /do_you_know/dimension.shtml   (1290 words)

 Imagining the Tenth Dimension - A Book by Rob Bryanton As we’re now imagining the ninth dimension, the same rules would apply – if we were to be able to instantaneously jump from one eighth dimensional line to another, it would be because we were able to fold through the ninth dimension. When we imagined the fourth dimension, it was as if we were treating the entirety of three-dimensional space in a particular state as a single point, and drawing a fourth-dimensional line to another point representing space as it is in a different state. Then in the seventh dimension, we treated all of the possible timelines which could be generated from our big bang as if this were a single point, and imagined drawing a line to a point representing all of the possible timelines for a completely different universe. www.tenthdimension.com /flash2.php   (3272 words)

 Thinking Man Software - Dimension 4 v5.0 Simply put, Dimension 4 v5.0 is the fastest and easiest way to synchronize your PC's clock for Windows-based operating systems. Dimension 4 uses one of a few well known and broadly implemented internet protocols to connect with publicly available time servers that have been operating on the Internet for over 15 years. At an interval you specify, Dimension 4 connects to a time server that you choose from an exhaustive list of time servers. www.thinkman.com /dimension4   (310 words)

 Elias Digests — dimension All of these dimensions are, in a figurative manner of speaking, subdivisions of what you view as your officially accepted dimension. As I have stated from the onset of this forum, this particular physical dimension is one of the most diverse and complex of all of the physical dimensions. You manifest within this dimension of physical focus, but within this dimension of physical focus there are many other dimensions of time fragments, for all of the time frameworks are simultaneous in actuality, but you separate them into different dimensions of time. www.eliasforum.org /digests/dimension.html   (4785 words)

 Dimension Printing   (Site not responding. Last check: ) Dimension SST and Dimension are powered by the company’s Catalyst™ software, which runs on workstations using Windows NT, 2000 or XP. The Dimension 3D Printing Group is a business unit of Stratasys, Inc., based in Minneapolis, Minn. Dimension 3D printers --–– which include the legacy Dimension and the enhanced Dimension SST –– are networked, desktop modeling systems that provide CAD (Computer-Aided-Design) users a fast, office-friendly, low-cost alternative for building functional 3D prints. Dimension 3D printers build accurate models layer by layer using durable ABS plastic, allowing users to not only evaluate design concepts, but test 3D prints for functionality, form and fit. www.dimensionprinting.com /news_pr_sst.html   (633 words)

 3.2 Topological Dimension The dimension on any other space will be defined as one greater that the dimension of the object that could be used to completely separate any part of the first space from the rest. The dimension of a space should be the maximum of its local dimensions where the local dimension is defined as one more than the dimension of the lowest dimensional object with the capacity to separate any neighborhood of the space into two parts. In other words, an object with topological dimension one can be transformed into an object with topological dimension two through a procedure that should not allow for such an occurrence. hypertextbook.com /chaos/32.shtml   (858 words)

 Dimension Album Discography The Dimension label was formed by Don Kirshner in 1962 in New York City. The song gave Dimension a number one hit on their first release in the summer of 1962. Dimension Records continued to issue 45s into 1965, when Kirschner sold the label to Columbia Pictures. www.bsnpubs.com /dimension.html   (845 words)

 USGS Minerals Information: Dimension Stone Dimension stone can be defined as natural rock material quarried for the purpose of obtaining blocks or slabs that meet specifications as to size (width, length, and thickness) and shape. Although a variety of igneous, metamorphic, and sedimentary rocks are used as dimension stone, the principal rock types are granite, limestone, marble, sandstone, and slate. Other varieties of dimension stone that are normally considered to be special minor types include alabaster (massive gypsum), soapstone (massive talc), and various products fashioned from natural stone. minerals.usgs.gov /minerals/pubs/commodity/stone_dimension   (182 words)

 DIMENSION: A dimension consists of the dimension entity, which contains the control parameters for the dimension, and a block definition which contains the entities defining the visual representation of the block. For angular dimensions, defpt2 and defpt3 are the endpoints of the first extension line. For diameter dimensions, defpt4 is the point selected on the circle or arc being dimensioned. www.opendwg.org /Library/ad2/reference/onlineref20/odtre433.htm   (483 words)

 3.3 Fractal Dimension This does not agree with the topological dimension of 1 but neither is it 2. Its dimension is not a whole number but a fraction. A study of twelve definitions of dimension appeared in 1981 (see Harrison) and an entire book on Dimension Theory was written in 1941 (Hurewicz and Wallman). hypertextbook.com /chaos/33.shtml   (1028 words)

 Fourth Dimension: Tetraspace While people generally call time the 4th dimension in the universe we live in, time will be the 5th dimension in my hypothetical universe. I rewrote the introduction to the fourth dimension, and changed one of the images. I made a number of changes to the fourth dimension glossary to fix errors that Polyhedron Dude pointed out, plus added some new words, bringing the total number of words from 102 to 106. tetraspace.alkaline.org   (566 words)

 Fractals & the Fractal Dimension This generalized treatment of dimension is named after the German mathematician, Felix Hausdorff. In general, the "rougher' the line, the steeper the slope, the larger the fractal dimension. A strange attractor is a fractal, and its fractal dimension is less than the dimensions of its phase space. www.vanderbilt.edu /AnS/psychology/cogsci/chaos/workshop/Fractals.html   (887 words)

 Dimension Systems Inc Corporate Site Dimension Systems has been built on a foundation of values based around fierce loyalty to our customers and employees. We are proven leaders in the IT industry and strongly believe that our success will always depend on being smart businesspeople focusing on helping our customers be more competitive and successful in today's tough business climate. VAR: Value Added Reseller - Dimension Systems is considered the premier VAR by some of the most recognized names in the Information Technology field. www.dimension-systems.com /company.htm   (166 words)

 Dimension Systems Inc Corporate Site Dimension Systems is always in the market for uniquely qualified salespeople who have an I/T technical background as well as the skills necessary to communicate the value that Dimension can provide to customers. Our customers are the lifeblood of Dimension Systems, and having the right people to always do what's right for our customers is critical to our success. Dimension Systems is looking for people who have solid administrative skills required to run a successful company. www.dimension-systems.com /careers.htm   (400 words)

 Dimension Studios -> Contest Rules. Dimension Studios together with our sponsor CTR clan will be conducting a Counter-Strike:Source Mapping Contest between June 1st and August 31st 2006. First, second, and third place winners will be awarded monetary prizes and their work will receive headline attention on several major sites. Each competitor, who is not a DS member, must register on Dimension Studios forums and pay a one time \$5 fee to enter. www.dimensionstudios.org /forum/index.php?showtopic=543   (506 words)

 The Fifth Dimension Bio by Mike Tatsui The Original 5th Dimension reunited throughout the 90's and decided to call it quits at the end of that decade. In 1991 The Original 5th Dimension received a Star on Hollywood’s Walk Of Fame which is located at the famed Roosevelt Hotel across from Mann’s Chinese Theater. The members in the group are into their own careers but they all seem to find the time to continue touring together and performing regularly with symphonies, on luxury cruises and all over the world to satisfy their many fans. members.aol.com /laruemccoo/fifthbio.htm   (3472 words)

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