In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point <math>A<math> called the origin. The number <math>c<math> 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 <math>A<math> and a real number <math>c<math> (possibly negative). The homothety <math>h_{A,c}<math> maps any point <math>M<math> to a point <math>M'<math> such that <math>A-M'=c(A-M)<math> (as vectors).

A homothety is an affine transformation and more precisely a similarity transformation. It multiplies all distances by <math>|c|<math>, all surfaces by <math>c^2<math>, etc.

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