Dilation (mathematics)

Dilation (mathematics)

In mathematics, a dilation is a function ƒ 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.

ee also

* homothety
* Dilation (operator theory)
* Dilation (non-mathematical uses)


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