Dilation (metric space)

In mathematics, a dilation is a function f from a metric space into itself that satisfies the identity

for all points ( x , y ) , where d ( x , y ) is the distance from x to y and r 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.