In mathematics, a dilation is a function <math>f</math> from a metric space <math>M</math> into itself that satisfies the identity
:<math>d(f(x),f(y))=rd(x,y)</math>
for all points <math>x, y \in M</math>, where <math>d(x, y)</math> is the distance from <math>x</math> to <math>y</math> and <math>r</math> 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.
See also
- Homothety
- Dilation (operator theory)