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Dilation (metric space)

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

for all points , where is the distance from to and is some positive real number.[1]

In Euclidean space, such a dilation is a similarity of the space.[2] 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[3] that is called the center of dilation.[4] Some congruences have fixed points and others do not.[5]

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