title: Dilation (metric space)
text: # Dilation (metric space)
  
  In mathematics, a dilation is a function $f$ from a metric space $M$ into itself that satisfies the identity
  
      $d(f(x),f(y))=rd(x,y)$
  
  for all points $x,y\in M$, 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.
  
  