Английская Википедия:Dilation (metric space)

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In mathematics, a dilation is a function <math>f</math> from a metric space <math>M</math> into itself that satisfies the identity

<math>d(f(x),f(y))=rd(x,y)</math>

for all points <math>x, y \in M</math>, where <math>d(x, y)</math> is the distance from <math>x</math> to <math>y</math> and <math>r</math> 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

Шаблон:Reflist