Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a homothety (or homothecy or non-rotating dilation) is a transformation of space which takes each line into a parallel line (in essence, a similarity that allows reflection in a single point, but otherwise preserves orientation). All homotheties form a group in either affine or Euclidean geometry. Congruent examples of homotheties are translations, reflections, and the identity transformation. In Euclidean geometry, when not a congruence, there is a unique number c by which distances in the dilatation are multiplied. It is called the ratio of magnification or dilation factor or scale factor or similitude ratio. Such a transformation can be called an enlargement. More generally c can be negative; in that case it not only multiplies all distances by | c | , but also inverts all points with respect to the fixed point.

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