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.
Choose an origin or center A and a real number c (possibly negative). The homothety hA,c maps any point M to a point M' such that A - M' = c(A - M) (as vectors).
A homothety is an affine transformation and more precisely a similarity transformation. It multiplies all distances by | c | , all surfaces by c2, etc.
See also: dilation (mathematics).