f
M
d(f(x),f(y))=rd(x,y)
x,y\inM
d(x,y)
x
y
r
In Euclidean space, such a dilation is a similarity of the space.[2] 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[3] that is called the center of dilation.[4] Some congruences have fixed points and others do not.[5]