Homothety

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 $\mathbf {AM'} =c\mathbf {AM}$ (vectors here). In other words, $A,M,M'$ are aligned and the (algebraic) distance $AM'$ is $c$ times the distance $AM$. (Algebraic means here that sign matters; for instance if $c=-1$ then $\mathbf {AM'} =-\mathbf {AM}$, which means that $M'$ is on the other side of $A$.)

A homothety is an affine transformation and more precisely a similarity transformation. It multiplies all distances by $c$, all surfaces by $c^{2}$, etc.

A homothety carries small people (aka avi) to large people (aka penev) via a rigorous course of castration