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hypercube    
超立方體; 超正方體

超立方體; 超正方體

hypercube
超立方體結構

hypercube
超立方

hypercube \hypercube\ n.
A mathematical object existing in more than three dimensions,
analogous to the cube in that each two-dimensional facet of
the surface is a square; a generalization of a cube in more
than three dimensions.
[PJC]

A cube of more than three dimensions. A single (2^0 = 1)
point (or "node") can be considered as a zero dimensional
cube, two (2^1) nodes joined by a line (or "edge") are a one
dimensional cube, four (2^2) nodes arranged in a square are a
two dimensional cube and eight (2^3) nodes are an ordinary
three dimensional cube. Continuing this geometric
progression, the first hypercube has 2^4 = 16 nodes and is a
four dimensional shape (a "four-cube") and an N dimensional
cube has 2^N nodes (an "N-cube"). To make an N1 dimensional
cube, take two N dimensional cubes and join each node on one
cube to the corresponding node on the other. A four-cube can
be visualised as a three-cube with a smaller three-cube
centred inside it with edges radiating diagonally out (in the
fourth dimension) from each node on the inner cube to the
corresponding node on the outer cube.

Each node in an N dimensional cube is directly connected to N
other nodes. We can identify each node by a set of N
{Cartesian coordinates} where each coordinate is either zero
or one. Two node will be directly connected if they differ in
only one coordinate.

The simple, regular geometrical structure and the close
relationship between the coordinate system and binary numbers
make the hypercube an appropriate topology for a parallel
computer interconnection network. The fact that the number of
directly connected, "nearest neighbour", nodes increases with
the total size of the network is also highly desirable for a
{parallel computer}.

(1994-11-17)

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英文字典中文字典相關資料:
  • Hypercube - Wikipedia
    In geometry, a hypercube is an n -dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract
  • Tesseract - Wikipedia
    In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube [1] Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles
  • Hypercubes - Math is Fun
    The general idea of a cube in any dimension is called a hypercube, or n-cube A 0-cube is a point, a 1-cube is a line, a 2-cube is a square, a 3-cube is a cube, etc Points, Lines, Surfaces, The magic binomial x+2 can tell us how many points, lines, surfaces etc for each dimension:
  • Hypercube graph - Wikipedia
    In graph theory, the hypercube graph Q n is the graph formed from the vertices and edges of an n-dimensional hypercube For instance, the cube graph Q 3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube
  • Hypercube -- from Wolfram MathWorld
    The hypercube is a generalization of a 3-cube to n dimensions, also called an n-cube or measure polytope It is a regular polytope with mutually perpendicular sides, and is therefore an orthotope It is denoted gamma_n and has Schläfli symbol {4,3,3_()_(n-2)}
  • Hypercube - Simple English Wikipedia, the free encyclopedia
    A hypercube is a closed, compact, convex figure that is made of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length An n -dimensional hypercube is also called an n-cube or an n-dimensional cube
  • Tesseract | Brilliant Math Science Wiki
    A tesseract, also known as a hypercube, is a four-dimensional cube, or, alternately, it is the extension of the idea of a square to a four-dimensional space in the same way that a cube is the extension of the idea of a square to a three-dimensional space
  • What Is a Tesseract or Hypercube? - Science Notes and Projects
    A tesseract or hypercube is the four-dimensional equivalent to a cube In three dimensions, it is like a cube within a cube, except if all the vertices were connected by 90 degree angles
  • Hypercube - Art of Problem Solving
    As used in geometry, a hypercube is an extrapolation of the cube or square to n dimensions When n is not specified, it's generally assumed to be 4 For example, a 4th dimensional hypercube is called a tesseract Therefore, an n-dimensional hypercube is also known as an n-cube It is best drawn and represented in non-Euclidean geometry Tesseract
  • Hypercube - Polytope Wiki
    A hypercube is the simplest center-symmetric polytope in each respective dimension, by facet count Hypercubes are a direct generalization of squares and cubes to higher dimensions





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