Two subsets \(X\) and \(Y\) of Euclidean metric space \(\mathbb R^n\) are called similar, if there exist a real number \( c > 0\), called the scaling constant, such that \(X\) is congruent to the subset \(Y'\) obtained from \(Y\) by multiplying each point \(A\in Y\) by the scaling constant
\[X\sim Y'=c\cdot Y.\]
Thus, \(X\) can be obtained from \(Y\) by uniformly scaling (enlarging or shrinking) \(Y\), possibly with additional Euclidean movements, like translation, rotation and reflection.
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