Dilation (metric space) explained

f

from a metric space

M

into itself that satisfies the identity

d(f(x),f(y))=rd(x,y)

for all points

x,y\inM

, where

d(x,y)

is the distance from

x

to

y

and

r

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

Notes and References

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  2. . See in particular p. 110.
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