Dilation (metric space)
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(Redirected from Dilation (mathematics))
In mathematics, a dilation is a function ƒ from a metric space into itself that satisfies the identity
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.
[edit] See also
- homothety
- Dilation (operator theory)
- Dilation (non-mathematical uses)
