Grupul omotetiilor în plan
The group of Homotheties in plan. Homothety

Summary/Abstract: This paper tries to explain some geometric transformations, which are also named homotheties. In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio. These are precisely the affine transformations with the property that the image of every line L is a line parallel to L. In projective geometry, a homothetic transformation is a similarity transformation(i.e., fixes a given elliptic involution) that leaves the line at infinity point‑wise invariant. In Euclidean geometry, a homothety of ratio λ multiplies distances between points by |λ| and all areas by λ2. The first number is called the ratio of magnification or dilation factor or scale factor or similitude ratio. Such a transformation can be called an enlargement if the scale factor exceeds 1. The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude.

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