The Similarity Geometry is the geometry \(({{\mathbb R}}^n, S(n))\) , where \(S(n)\) is the group of similarities of \({{\mathbb R}}^n\) . This geometry is broader than the Euclidean Geometry, in the sense that it contains it, but the \(S(n)\) -properties are fewer than the \(E(n)\) -properties. In Euclidean Geometry, similarity refers to objects of the same shape but possibly different size.