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.. See in particular p. 110. 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..

See also

Homothety Dilation (operator theory)

References