Definitions

# Dilation (mathematics)

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

$d\left(f\left(x\right),f\left(y\right)\right)=rd\left(x,y\right) ,$

for all points xy, where d(xy) is the distance from x to y and r 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.