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 | + | {{TEX|done}} |
| + | 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 | ||
| − | + | $$x'=x,\quad y'=ky,\quad k>0.$$ | |
| − | A contraction of space towards the | + | A contraction of space towards the $xy$-plane, parallel to the $z$-axis, is given by the relations |
| − | + | $$x'=x,\quad y'=y,\quad z'=kz,\quad k>0.$$ | |
Latest revision as of 07:14, 23 August 2014
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
$$x'=x,\quad y'=ky,\quad k>0.$$
A contraction of space towards the $xy$-plane, parallel to the $z$-axis, is given by the relations
$$x'=x,\quad y'=y,\quad z'=kz,\quad k>0.$$
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=15206
Contraction(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contraction(2)&oldid=15206
This article was adapted from an original article by N.V. Reveryuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article