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Homothety

From Biocrawler, the free 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.

Choose an origin or center $A$ and a real number $c$ (possibly negative). The homothety $h A, c$ 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 $c 2$ , etc.