In
mathematics, a
homothety (or
homothecy, or
homogeneous dilation) is a
transformation of an
affine space determined by a point
S called its
center and a nonzero number
λ called its
ratio, which sends
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=1014)
in other words it fixes
S, and sends any
M to another point
N such that the segment
SN is on the same line as
SM, but scaled by a factor
λ. In
Euclidean geometry homotheties are the
similarities that fix a point and either preserve (if ) or reverse (if ) the direction of all vectors. Together with the
translations, all homotheties of an affine (or Euclidean) space form a
group, the group of
dilations or
homothety-translations. These are precisely the
affine transformations with the property that the image of every line
L is a line
parallel to
L.