Dilation (metric space)

From formulasearchengine
Jump to navigation Jump to search

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]

See also

References

  1. {{#invoke:citation/CS1|citation |CitationClass=citation }}.
  2. {{#invoke:citation/CS1|citation |CitationClass=citation }}. See in particular p. 110.
  3. {{#invoke:citation/CS1|citation |CitationClass=citation }}.
  4. {{#invoke:citation/CS1|citation |CitationClass=citation }}.
  5. {{#invoke:citation/CS1|citation |CitationClass=citation }}.