Dilation - Definition and Overview

Dilation is the act of expanding something. This term is usually used by doctors in the context of "dilating the pupils", dilation of blood vessels (vasodilation), or dilation of the cervix in childbirth.

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

<math>d(f(x),f(y))=rd(x,y)<math>

where d(x,y) is the distance from x to y and r is some real number. A dilation of a Euclidean space is called a similarity.