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 positive real number.
Dilation is yet another name for similarity of a Euclidean space. Another way to look at a dilation is as a transformation that changes the size but not the shape of an object or figure. Every dilation that is not a congruence has a fixed point that is called the center of dilation.
See also
- homothety
- Isometric dilation
- Unitary dilation
- Dilation (non mathematical uses)
