Difference between revisions of "Unit cube"

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en>Tamfang
(add a necessary condition; remove something not distinctive of *unit* cubes; split a paragraph of two unrelated sentences)
 
en>Cydebot
 
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Sometimes the term "unit cube" refers in specific to the set [0,&nbsp;1]<sup>''n''</sup> of all ''n''-tuples of numbers in the interval [0,&nbsp;1].<ref name="pcm"/>
Sometimes the term "unit cube" refers in specific to the set [0,&nbsp;1]<sup>''n''</sup> of all ''n''-tuples of numbers in the interval [0,&nbsp;1].<ref name="pcm"/>


The length of the longest diagonal of a unit hypercube of ''n'' dimensions is <math>\sqrt n</math>, the square root of ''n'' and the (Euclidean) length of the vector ''(1,1,1,....1,1)'' in ''n''-dimensional space.<ref name="cbm"/>
The length of the longest diagonal of a unit hypercube of ''n'' dimensions is <math>\sqrt n</math>, the square root of ''n'' and the (Euclidean) length of the vector (1,1,1,....1,1) in ''n''-dimensional space.<ref name="cbm"/>


== See also ==
== See also ==
*[[K-cell (mathematics)|K-cell]]
*[[Robbins constant]], the average distance between two random points in a unit cube
*[[Robbins constant]], the average distance between two random points in a unit cube
*[[Tychonoff cube]], an infinite-dimensional analogue of the unit cube
*[[Tychonoff cube]], an infinite-dimensional analogue of the unit cube
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[[Category:Euclidean solid geometry]]
[[Category:Euclidean solid geometry]]
[[Category:One]]
[[Category:1 (number)]]
[[Category:Cubes]]
[[Category:Cubes]]


{{Elementary-geometry-stub}}
{{Elementary-geometry-stub}}

Latest revision as of 22:01, 28 November 2014

Unit cube

A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.[1][2] The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.[3]

Unit hypercube

The term unit cube or unit hypercube is also used for hypercubes, or "cubes" in n-dimensional spaces, for values of n other than 3 and edge length 1.[1][2]

Sometimes the term "unit cube" refers in specific to the set [0, 1]n of all n-tuples of numbers in the interval [0, 1].[1]

The length of the longest diagonal of a unit hypercube of n dimensions is , the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space.[2]

See also

References

  1. 1.0 1.1 1.2 {{#invoke:citation/CS1|citation |CitationClass=citation }}. See in particular p. 671.
  2. 2.0 2.1 2.2 {{#invoke:citation/CS1|citation |CitationClass=citation }}.
  3. {{#invoke:citation/CS1|citation |CitationClass=citation }}.

External links

Template:Elementary-geometry-stub