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hypercube    
超立方体; 超正方体

超立方体; 超正方体

hypercube
超立方体结构

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关资料:


  • 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
  • Hypercubes - Math is Fun
    In Geometry we can have different dimensions The general idea of a cube in any dimension is called a hypercube, or n-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
  • 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
  • What Is a Hypercube? From Cubes to Tesseracts - ScienceInsights
    A hypercube is the extension of a square and a cube into higher dimensions Just as a cube is a 3D version of a 2D square, a hypercube (most commonly referring to the 4D version, called a tesseract) is what you get when you push a cube into a fourth spatial dimension
  • Hypercube - Polytope Wiki
    A hypercube is a polytope generalizing the notion of the square, cube, tesseract, etc to arbitrary dimensions It is the simplest centrally-symmetric polytope in each respective dimension, by facet count
  • 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
  • Counting the Faces of Higher-Dimensional Cubes
    Analogous to the sequence of simplexes in each dimension, we have a sequence of cubes We begin a table Moving a cube perpendicular to itself creates a hypercube When we try to fill in the missing numbers for a hypercube, the process becomes a bit more difficult
  • Interactive 4D Handbook - 4D Cubes - Bailey Snyder
    To build a 4D cube, let’s start all the way back with a simple 1D line Drag that line along the y axis to create a 2D square Drag that square along the z axis to create a 3D cube And finally, drag that cube along the w axis to create a 4D hypercube!





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