Namespaces
Variants
Actions

Contraction(2)

From Encyclopedia of Mathematics
Revision as of 17:11, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

An affine transformation of the plane under which each point is shifted towards the -axis, parallel to the -axis, by a distance proportional to its ordinate. In a Cartesian coordinate system a contraction is given by the relations

A contraction of space towards the -plane, parallel to the -axis, is given by the relations


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=19336
This article was adapted from an original article by N.V. Reveryuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article