Dilation (metric space)

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

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

for all points (x,y) where d(x,y) 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.

See also

• homothety
• Dilation (operator theory)