Directly Similar

Two figures are said to be similar when all corresponding angles are equal, and are directly similar when all corresponding angles are equal and described in the same rotational sense.

Any two directly similar figures are related either by a translation or by a spiral similarity (Coxeter and Greitzer 1967, p. 97).

See also

Douglas-Neumann Theorem, Fundamental Theorem of Directly Similar Figures, Homothetic, Inversely Similar, Similar, Spiral Similarity

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References

Casey, J. "Two Figures Directly Similar." Supp. Ch. §2 in A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 173-179, 1888.Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 95, 1967.Lachlan, R. "Properties of Two Figures Directly Similar" and "Properties of Three Figures Directly Similar." §213-219 and 223-143 in An Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 135-138 and 140-143, 1893.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 12, 1991.

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Directly Similar

Cite this as:

Weisstein, Eric W. "Directly Similar." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DirectlySimilar.html

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