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.