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 $|c|$, but also inverses all points with respect to the fixed point.

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 $M\text{'}$ such that

$A-M\text{'}=c(A-M)$

(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 $|c|$, all surface areas by $c^2$, etc.

See also: dilation (mathematics).

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• Homothety

Geometry

Homothetie | Homotecia | Homothétie | Omotetia | Jednokładność | Гомотетия