about the mathematical concept the film Cube 2 Hypercube align right class wikitable Perspective projection ... , a hypercube is an n dimensional analogue of a Square geometry square n 2 and a cube n 3 . It is a Closed ... s dimension s, perpendicular to each other and of the same length. An n dimensional hypercube ... Hyperspaces Emanuel Lodewijk dp 141817968X ref , but it has now been superseded. The hypercube is the special case of a hyperrectangle also called an orthotope . A unit hypercube is a hypercube whose side has length one unit. Often, the hypercube whose corners or vertices are the 2 sup n sup points in R sup n sup with coordinates equal to 0 or 1 is called the unit hypercube . Construction Image ... &ndash A point is a hypercube of dimension zero. 1 &ndash If one moves this point one unit length, it will sweep out a line segment, which is a unit hypercube of dimension one. 2 &ndash If one moves this line ... dimension, it generates a 4 dimensional unit hypercube a unit tesseract . This can be generalized ... as a Minkowski sum the d dimensional hypercube is the Minkowski sum of d mutually perpendicular ... skeleton of a hypercube is a hypercube graph . Coordinates A unit hypercube of n dimensions is the convex ... hypercube is also often regarded as the convex hull of all sign permutations of the coordinates ... number of dimensions. The hypercube offset family is one of three regular polytope families, labeled by Coxeter as sub n sub . The other two are the hypercube dual family, the cross polytope s , labeled ... . Elements A hypercube of dimension n has 2 n sides a 1 dimensional line has 2 end points a 2 dimensional ... dimensional tesseract has 8 cell geometry cell s . The number of vertices points of a hypercube ... of n 2 faces in an n dimensional hypercube is math 2n 2 2n math The number of m dimensional hypercubes ... in total. class wikitable Hypercube elements math E m,n math m 0 1 2 3 4 5 6 7 8 9 10 polytope n ... 20 1 Graphs An n cube can be projected inside a regular 2n gonal polygon by a Petrie polygon The hypercube ... more details
infobox graph name Hypercube graph image Image Hypercubestar.svg 200px image caption The hypercube graph ... graph Hamiltonian notation Q sub n sub In graph theory , the hypercube graph Q sub n sub is a regular ... that the hypercube graph is the one dimensional skeleton topology skeleton of the geometric hypercube . Hypercube graphs should not be confused with cubic graph s, which are graphs that are 3 regular. The only hypercube that is a cubic graph is Q sub 3 sub . Construction File Hypercube construction.gif thumb left An animation showing the construction of a hypercube graph of dimension 4 The hypercube ... Properties Hamiltonicity It is a well known fact that every hypercube Q sub n sub is hamiltonian ... induction and the inductive construction of hypercube graphs. Hamiltonicity of the hypercube ... between the set of n bit cyclic Gray codes and the set of Hamiltonian cycles in the hypercube ... in the hypercube extends to a Hamiltonian cycle. ref citation first J. last Fink title Perfect ... to Hamiltonian cycles in hypercubes on Open Problem Garden. 2007. ref Bipartiteness Every hypercube ... The hypercube graph Q sub n sub n 1 is the Hasse diagram of a finite Boolean algebra structure Boolean algebra . is a median graph . Every median graph is an partial cube isometric subgraph of a hypercube , and can be formed as a retraction of a hypercube. has more than 2 sup 2 sup n 2 sup sup ... transitive graph arc transitive and Symmetric graph symmetric . The symmetries of hypercube graphs ... of finding the longest path or cycle that is an induced subgraph of a given hypercube graph is known as the snake in the box problem. Szymanski s conjecture concerns the suitability of a hypercube as an network ... each hypercube vertex to another vertex with which it should be connected, there is always ... Switched Hypercube location Silver Spring, MD pages 103 110 publisher IEEE Computer Society Press ... Q sub 4 sub is the Levi graph of the M bius configuration . See also commonscat Hypercube graphs ... more details
Merge from Magic tesseract discuss Talk Magic hypercube Merge from 4 date November 2010 Merge from Nasik magic hypercube discuss Talk Magic hypercube Nasik date November 2010 technical date October 2010 Refimprove date October 2010 In mathematics , a magic hypercube is the dimension k dimensional generalization ... as the main space diagonal s is equal to a single number, the so called magic constant of the hypercube , denoted M sub k sub n . It can be shown that if a magic hypercube consists of the numbers 1 ... on every cross section geometry cross section diagonal also sum up to the hypercube s magic number, the hypercube is called a perfect magic hypercube otherwise, it is called a semiperfect magic hypercube . The number n is called the order of the magic hypercube. Five , six , seven and eight ... proved the following theorem A p dimensional magic hypercube of order n exists if and only if p 1 and n is different from 2 or p 1. A construction of a magic hypercube follows from the proof. The R ... order of a hypercube with the letter m . n Dimension the number of directions within a hypercube. m Order the number of numbers along a direction. Further In this article the analytical ... add 1 to each number. This has absolutely no effect on the properties of the hypercube. Notations ... within the hypercube < sub k sub i k 0..n 1 i 0..m 1 > vector through the hypercube Note The notation ... multiples of m, as the magic hypercube resides in n dimensional modular space. There can be multiple ... to specify a particular line within the hypercube see r agonal in pathfinder section Note ... into the hypercube sup n sup H sub m sub sub k 0 sub sup n 1 sup LP sub k sub m sup k sup ... places especially p section Both methods fill the hypercube with numbers, the knight jump guarantees .... Aspects A hypercube knows n 2 sup n sup Aspectial variants, which are obtained by coordinate ... equal. Thus any hypercube can be represented shown in normal position by sub k sub 0 min sub k sub ... more details
Latin hypercube sampling LHS is a statistics statistical method for generating a distribution of plausible collections of parameter values from a multidimensional distribution . The Sampling statistics sampling method is often applied in uncertainty analysis. The technique was first described by McKay in 1979. ref name C3M cite journal last McKay first M.D. coauthors Beckman, R.J. Conover, W.J. year 1979 month May title A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code journal Technometrics volume 21 issue 2 pages 239 245 publisher American Statistical Association issn 0040 1706 doi 10.2307 1268522 format JSTOR Abstract laysummary laysource laydate quote osti 5236110 jstor 1268522 ref It was further elaborated by Ronald L. Iman , and others ref cite journal last Iman first R.L. coauthors Helton, J.C. and James Edward Campbell Campbell, J.E. title An approach to sensitivity analysis of computer models, Part 1. Introduction, input variable selection and preliminary variable assessment journal Journal of Quality Technology ... hypercube sampling program user s guide year 1980 osti 5571631 ref In the context of statistical sampling ... sample in each row and each column. A Latin hypercube is the generalisation of this concept to an arbitrary ... the Latin hypercube requirements note that this forces the number of divisions, math M math , to be equal ... so far. The maximum number of combinations for a Latin Hypercube of math M math divisions and math ... M n right N 1 M N 1 math For example, a Latin hypercube of math M 4 math divisions with math N 2 math variables i.e., a square will have 24 possible combinations. A Latin hypercube of math M 4 math divisions ... random sampling, Latin Hypercube sampling and orthogonal sampling can be explained as follows In random .... In Latin Hypercube sampling one must first decide how many sample points to use and for each sample ... Hypercube sample and that each subspace is sampled with the same density. Thus, orthogonal ... more details
Merge to Magic hypercube discuss Talk Magic hypercube Nasik date November 2010 A Nasik magic hypercube is a magic hypercube with the added restriction that all possible lines through each cell sum correctly to math S frac m m n 1 2 math where S the magic constant, m the order and n the dimension, of the hypercube. Or, to put it more concisely, all pan r agonals sum correctly for r 1... n . The above definition is the same as the Hendricks definition of perfect , but different than the Boyer Trump definition. See Perfect magic cube Because of the confusion over the term perfect when used with reference to magic squares, magic cubes, and in general magic hypercubes, I am proposing the above as an unambiguous term . Following is an attempt to use the magic cube as a specific example. A Nasik magic cube is a magic cube with the added restriction that all 13 m sup 2 sup possible lines sum correctly to the magic constant. This class of magic cube is commonly called perfect John Hendricks definition. . See Magic cube classes . However, the term perfect is ambiguous because it is also used for other types of magic cubes. Perfect magic cube demonstrates just one example of this. br The term nasik would apply to all dimensions of magic hypercubes in which the number of correctly summing paths lines through any cell of the hypercube is P 3 sup n sup 1 2 A pandiagonal magic square then would be a nasik square because 4 magic line pass through each of the m sup 2 sup cells. This was A.H. Frost s original definition of nasik. br A nasik magic cube would have 13 magic lines passing through ... 4 ref Conclusion If the term nasik is adopted as the definition for a magic hypercube where all possible ... hypercubes contained in it are nasik Hendricks perfect . See also Magic hypercube Magic hypercubes ... A Magic Hypercube encyclopedia with a broad range of material http members.shaw.ca hdhcubes index.htm ... Categories DEFAULTSORT Nasik Magic Hypercube Category Recreational mathematics Category Magic squares ... more details
Summary Self made image demonstrating a hypercube. Licensing PD self date October 2006 Orphan image Copy to Wikimedia Commons bot Fbot ... more details
Summary Vector version available Snakeinthebox.svg Drawing of a snake in a three dimensional hypercube Licensing PD self date October 2006 Orphan image Copy to Wikimedia Commons bot Fbot ... more details
Image Unitcube.svg thumb 300px right Unit cube A unit cube , sometimes called a cube of side 1 , is a cube whose sides are 1 unit long. The volume of a 3 dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units. Unit Hypercube The term unit cube or unit hypercube is also used to refer to hypercube s, or cubes in n dimensional spaces, for values of n other than 3. In all dimensions, the unit cube has 2 sup n sup corners. Sometimes the term unit cube refers in specific to the set 0, 1 sup n sup of all n tuples of numbers in the interval 0, 1 . The length of the longest diagonal of a unit hypercube of n dimensions is the square root of n . See also Unit square Unit sphere External links mathworld urlname UnitCube title Unit cube Category Euclidean solid geometry Category One Category Cubes Elementary geometry stub es Cubo unitario it Cubo unitario he nl Eenheidskubus pt Cubo unit rio ru sl Enotska kocka sv Enhetskub zh ... more details
In mathematics, Szymanski s conjecture , named after harvs first Ted H. last Szymanski year 1989 txt , states that every permutation on the n dimensional doubly directed graph directed hypercube graph can be routed with edge disjoint Path graph theory paths . That is, if the permutation matches each vertex v to another vertex v , then for each v there exists a path in the hypercube graph from v to v such that no two paths for two different vertices u and v use the same edge in the same direction. Through computer experiments it has been verified that the conjecture is true for n 4 harv Baudon Fertin Havel 2001 . For n 5 there exist permutations that require the use of paths that are not shortest path s in order to be routed harv Lubiw 1990 . References citation last1 Baudon first1 Olivier last2 Fertin first2 Guillaume last3 Havel first3 Ivan doi 10.1016 S0166 218X 00 00386 3 issue 1 journal Discrete Applied Mathematics pages 43 58 title Routing permutations and 2 1 routing requests in the hypercube volume 113 year 2001 . citation last Lubiw first Anna doi 10.1016 0020 0190 90 90106 8 issue 2 journal Information Processing Letters pages 57 61 title Counterexample to a conjecture of Szymanski on hypercube routing volume 35 year 1990 . citation last Szymanski first Ted H. contribution On the Permutation Capability of a Circuit Switched Hypercube location Silver Spring, MD pages 103 110 publisher IEEE Computer Society Press title Proc. Internat. Conf. on Parallel Processing volume 1 year 1989 . Category Conjectures Category Graph theory Category Network topology math stub ... more details
correctly for r 1 and n , then we know that the magic hypercube is simple magic regardless of what dimension it is The length of an r agonal of a hypercube with side length a is math sqrt ra 2 math . See also Magic cube Magic hypercube Magic cube classes Hypotenuse References John R. Hendricks, The Pan ... more details
Flat Neighborhood Network FNN is a Network topology topology for distributed computing and other computer networks. Each Node networking node connects to two or more Network switch switches which, ideally, entirely cover the node collection, so that each node can connect to any other node in two hops jump up to one switch and down to the other node . This contrasts to toplogies with fewer cables per node which communicate with remote nodes via intermediate nodes, as in Hypercube see Connection Machine The Connection Machine . See also Thinking Machines Corporation built the Connection Machine employing hypercube topology for its compute nodes. Kentucky Linux Athlon Testbed Kentucky s Linux Athlon Testbed KLAT2 is an archetypal implementation. External links http aggregate.org FNN The Aggregate at the University of Kentucky defines FNN and includes a bibliography. Category Supercomputers compsci stub super compu stub ... more details
NCUBE may refer to People Ncube is a very common surname among the Ndebele people Zimbabwe Ndebele . Pius Ncube , former Roman Catholic Archbishop of Bulawayo, Zimbabwe Welshman Ncube , a leading member Movement for Democratic Change in Zimbabwe Ben Ncube , spokesman for the Zimbabwe National Army Trevor Ncube , Zimbabwean newspaper tycoon Other nCUBE Corporation &ndash and their parallel computers nCUBE 10, nCUBE 2 and nCUBE 3 Ncube satellite &ndash built by Norwegian students Hypercube of n dimensions. disambig ... more details
Merge to Magic hypercube discuss Talk Magic hypercube Merge from 4 date November 2010 In mathematics , a magic tesseract is the 4 dimensional counterpart of a magic square and magic cube , that is, a number of integers arranged in an n × n × n × n pattern such that the sum of the numbers on each pillar along any axis as well as the main space diagonal s is equal to a single number, the so called magic constant of the tesseract , denoted M sub 4 sub n . It can be shown that if a magic tesseract consists of the numbers 1, 2, ..., n sup 4 sup , then it has magic constant OEIS id A021003 math M 4 n frac n n 4 1 2 . , math The number n is called the order of the magic tesseract. Perfect magic tesseract If, in addition, the numbers on every cross section geometry cross section diagonal also sum up to the tesseract s magic constant, the tesseract is called a perfect magic tesseract otherwise, it is called a semiperfect magic tesseract . Alternative Definition The above assumes that one of the older definitions for perfect magic cubes is used. See Magic Cube Classes . The Universal Classification System for Hypercubes John R. Hendricks requires that for any dimension hypercube, all possible lines sum correctly for the hypercube to be considered perfect magic. Because of the confusion with the term perfect , nasik is now the preferred term for any magic hypercube where all possible lines sum to S . Nasik was defined in this manner by C. Planck in 1905. A nasik magic tesseract has 40 lines of m numbers passing through each of the m sup 4 sup cells. The smallest possible nasik magic tesseract is of order 16 its magic constant is 524296. The first one was discovered by retired meteorologist John R. Hendricks from British Columbia in 1999 with the help of Cliff Pickover ... time on an IBM IntelliStation computer system. See also Magic hypercube Magic hypercubes Nasik magic hypercube John R. Hendricks References Andrews, W.S., Magic Squares and Cubes , Dover, Publ ... more details
Infobox Painting image file Dali Crucifixion hypercube.jpg title Crucifixion Corpus Hypercubus artist Salvador Dal year 1954 type oil painting oil on canvas height 194.3 width 123.8 museum Metropolitan Museum of Art , New York City Crucifixion Corpus Hypercube Hypercubus was painted in 1954 by Salvador Dal , and depicts the crucified Jesus upon the Net polyhedron net of a hypercube . Gala Dal Gala Salvador Dal Dal s wife , is the figure in the bottom left, who stands looking up to the crucified Jesus. The scene is depicted in front of the bay of Port Lligat . ref http www.theartistsalvadordali.com salvador dali painting poster print corpus hypercubus.htm Crucifixion Corpus Hypercubus at theartistsalvadordali.com ref ref http library.humboldt.edu art Artists Dali Salvador Dali Home.htm art inside the HSU library The Crucifixion ref The painting is in the Metropolitan Museum of Art in New York , United States USA . See also Tesseract Net polyhedron Salvador Dal References reflist Category Salvador Dal paintings Category Paintings depicting Jesus Category 1954 paintings Painting stub it Corpus Hypercubus no Korsfestelse Corpus Hypercubus pl Corpus Hypercubus ru ... more details
The Intel iPSC 860 was a massively parallel supercomputer launched by Intel in 1990. It followed the Intel iPSC 2 and was superseded by the Intel Paragon . The iPSC 860 consisted of up to 128 processing elements connected in a hypercube topology , each element consisting of an Intel i860 or Intel 386 microprocessor . External links http www.phy.ornl.gov csep CSEP IP IP.html CSEP iPSC 860 Guide Category Supercomputers Category Massively parallel computers Category Intel products Ipsc 860 super compu stub ko iPSC 860 it Intel iPSC 860 pl Intel iPSC 860 ru Intel iPSC 860 ... more details
A simple magic square is the lowest of two basic classes of magic square . It has the minimum requirements for a square to be considered magic. All lines parallel to the edges, plus the two main diagonals must sum to the magic constant. math S frac m m 2 1 2 . math The other class of magic square is most often called a pandiagonal magic square , but also sometimes it is called perfect or nasik . Of course, within these two main classes are a great many varieties of magic squares. See also Magic cube Magic cube classes Nasik magic hypercube Category Magic squares ... more details
Non free 2D art Non free media rationale Article Church of San Juan Ap stol y Evangelista, Santianes de Pravia Description A Propos of the Treatise on Cubic Form by Juan de Herrera , 1960 by Salvador Dal , 1910 . br This hypercube was inspired by the foundation stone of the church Silo princeps fecit Source http www.dali gallery.com html galleries painting22.htm www.dali gallery.com Portion It represents the complet work. Resolution It is a low resolution image. Purpose It illustrates an educational article about the painting that this image represents. Replaceability It is not replaceable with an uncopyrighted or freely copyrighted image of comparable educational value. other information Category Salvador Dal paintings Category Images of paintings ... more details
The Caltech Cosmic Cube was a Parallel computing parallel computer , developed by Charles Seitz and Geoffrey Fox from 1981 onward. ref Cosmic Cubism from Engineering & Science, March 1984 http calteches.library.caltech.edu 3419 1 Cubism.pdf ref It was an early attempt to capitalise on Very large scale integration VLSI to speed up scientific calculations at a reasonable cost. Using commodity hardware and an architecture suited to the specific task Quantum chromodynamics QCD , Fox and Seitz demonstrated that this was indeed possible. In 1987 several people in the group formed a company called Parasoft to commercialize the message passing interface developed for the Cosmic Cube. ref http wotug.org parallel documents misc timeline timeline.txt History of Supercomputing ref Characteristics 64 Intel 8086 Intel 8086 87 processors ref http www.netlib.org utk lsi pcwLSI text node13.html Birth of the Hypercube ref 128kB of memory per processor 6 dimensional hypercube network, i. e. each processor can directly exchange data with six other processors. References Reflist http caltechcstr.library.caltech.edu 297 01 5208 TR 86.pdf The Torus Routing Chip http netalive.startlogic.com debenedictis.org erik Parallel Computer Archival Documents John Apostolakis, Clive Baillie, Robert W. Clayton, Hong Ding, Jon Flower, Geoffrey C. Fox, Thomas D. Gottschalk, Bradford H. Hager, Herbert Keller Herbert B. Keller , Adam Kolawa Adam K. Kolawa , Steve W. Otto, Toshiro Tanimoto, Eric F. van de Velde, J. Barhen, J. R. Einstein, and C. C. Jorgensen. 1989. Supercomputer applications of the hypercube. In Supercomputing systems architectures, design, and performance, Svetlana P. Kartashev and Steven I. Kartashev Eds. . Van Nostrand Reinhold Co., New York, NY, USA 480 577. External links http resolver.caltech.edu CaltechCSTR 1988.cs tr 88 01 The C Programmer s Abbreviated Guide to Multicomputer Programming Parallel Computing Category Parallel computing ... more details
refimprove date November 2011 The Intel iPSC is a parallel computer . It was superseded by the Intel iPSC 2 . iPSC also more generally refers to the particular line of Intel parallel computers, which includes the iPSC 2 and the Intel iPSC 860 iPSC 860 . Acronym iPSC means Intel Personal SuperComputer . The iPSC 1 was introduced by Intel in 1985, and consisted of 32 to 128 nodes arranged in an ethernet connected hypercube. Each node had a 80286 CPU with 80287 math coprocessor, 512K of RAM , and eight ethernet ports seven for the hypercube , and one to talk to the cube manager . The system was hosted by a Personal Computer PC running Xenix , the cube manager . The basic models were the iPSC d5 five dimension hypercube, 32 nodes , iPSC d6 6d, 64 nodes , and iPSC d7 7d, 128 nodes . Extra memory iPSC MX and vector processor iPSC VX models were also available, in the three sizes. iPSC 1 was the first commercial parallel computer. ref http www.piercefuller.com collect other.html ref Characteristics Dimensions overall 127 cm x 41 cm x 43 cm Speed 2 M FLOPS Memory Width 16 bit ref http www.computerhistory.org revolution supercomputers 10 74 286 ref References references External links http www.piercefuller.com library 10166.html Photos of iPSC d5 model from private collection. super compu stub DEFAULTSORT Intel Ipsc Category Supercomputers Category Massively parallel computers Category Intel products Ipsc ru Intel iPSC ... more details
Ernie Barbarash is a movie producer, perhaps best known as co producer of the films American Psycho film American Psycho , Cube 2 Hypercube , Prisoner of Love , The First 9 Weeks and The Cat s Meow . Barbarash also wrote and directed Cube Zero and Stir of Echoes The Dead Speak . He also directed the Canadian horror thriller They Wait . Filmography Director The Package 2012 film The Package 2012 Six Bullets 2012 film Six Bullets 2012 Assassination Games 2011 Ticking Clock 2010 Rock the House film Rock the House 2010 Hardwired film Hardwired 2009 They Wait 2007 Stir of Echoes The Homecoming 2007 Cube Zero 2004 Producer Cube Zero 2004 executive producer Cube 2 Hypercube 2002 producer American Psycho II All American Girl 2002 producer The Cat s Meow 2001 co producer American Psycho film American Psycho 2000 co producer Prisoner of Love film Prisoner of Love 1999 producer The First 9 1 2 Weeks 1998 co producer The Incredible Adventures of Marco Polo on His Journeys to the Ends of the Earth 1998 co producer Writer Stir of Echoes The Homecoming 2007 written by Cube Zero 2004 written by Cube 2 Hypercube 2002 screenplay External links imdb name id 0053228 rotten tomatoes person id ernie barbarash Ernie Barbarash Persondata Metadata see Wikipedia Persondata . NAME Barbarash, Ernie ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Barbarash, Ernie Category American film directors Category Living people Category Year of birth missing living people US film director stub fr Ernie Barbarash it Ernie Barbarash fi Ernie Barbarash ... more details
of an infinite family of polytopes, called hypercube s. The Dual polytope dual of a 6 cube can be called ... top Image 6 cube column graph.svg 240px BR This hypercube graph is an orthogonal projection . This oriention ... 6D uniform polytopes polypeta o3o3o3o3o4x ax External links MathWorld title Hypercube urlname Hypercube ... Multi dimensional Glossary hypercube Garrett Jones Polytopes Category 6 polytopes Geometry stub ... more details
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