Dilation (metric space)
In mathematics, a dilation is a function 
from a metric space into itself that satisfies the identity
for all points 
where 
is the distance from 
to 
and 
is some positive real number.
In Euclidean space, such a dilation is a similarity of the space. Dilations change the size but not the shape of an object or figure.
Every dilation of a Euclidean space that is not a congruence has a unique fixed point that is called the center of dilation. Some congruences have fixed points and others do not.