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In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point called the origin. The number 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 and a real number (possibly negative). The homothety maps any point to a point such that (as vectors).
A homothety is an affine transformation and more precisely a similarity transformation. It multiplies all distances by , all surfaces by , etc.
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