Dilation (metric space)
In mathematics, a dilation is a function formula_1 from a metric space formula_2 into itself that satisfies the identity for all points formula_4, where formula_5 is the distance from formula_6 to formula_7 and formula_8 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. Dilation