Difference between revisions of "Contraction(2)"
From Encyclopedia of Mathematics
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− | An affine transformation of the plane under which each point is shifted towards the x-axis, parallel to the | + | An affine transformation of the plane under which each point is shifted towards the x-axis, parallel to the y-axis, by a distance proportional to its ordinate. In a Cartesian coordinate system a contraction is given by the relations |
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Revision as of 22:06, 27 March 2011
An affine transformation of the plane under which each point is shifted towards the x-axis, parallel to the y-axis, by a distance proportional to its ordinate. In a Cartesian coordinate system a contraction is given by the relations
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A contraction of space towards the -plane, parallel to the
-axis, is given by the relations
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Comments
More usually, a contraction is defined as a transformation of a metric space that reduces distances. The notion defined above has no established name in Western literature, but is sometimes called a compression or compression-expansion.
How to Cite This Entry:
Contraction(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contraction(2)&oldid=19337
Contraction(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contraction(2)&oldid=19337
This article was adapted from an original article by N.V. Reveryuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article