Definition: Similarity

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.

Corollaries: 1
Definitions: 2 3 4 5 6
Examples: 7
Proofs: 8
Propositions: 9 10 11 12 13 14 15
Sections: 16


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References

Bibliography

  1. Knerr, Richard: "Knaurs Buch der Mathematik", Droemer Knaur Lexikographisches Institut, M√ľnchen, 1989