Homothetic transformation
From Free net encyclopedia
In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point A called the origin. The number c by which distances are multiplied is called the dilation factor or similitude ratio. Such a transformation is also called an enlargement.
More generally c can be negative; in that case it not only multiplies all distances by <math>|c|</math>, but also inverses all points with respect to the fixed point.
Choose an origin or center A and a real number <math>c</math> (possibly negative). The homothety <math>h_{A,c}</math> maps any point M to a point <math>M'</math> such that
- <math>A-M'=c(A-M)</math>
(as vectors).
A homothety is an affine transformation (if the fixed point is the origin: a linear transformation) and also a similarity transformation. It multiplies all distances by <math>|c|</math>, all surface areas by <math>c^2</math>, etc.
See also: dilation (mathematics).
External link
de:Homothetie
es:Homotecia fr:Homothétie it:Omotetia pl:Jednokładność ru:Гомотетия