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# Spiral Similarity

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a spiral symmetry. In fact, any two directly similar figures are related either by a translation or by a spiral symmetry (Coxeter and Greitzer 1967, p. 97).

A spiral similarity tessellation of any ordinary tessellation can be constructed by placing a series of polygonal tiles of decreasing size on an equilateral spiral.

Affine Transformation, Central Dilation, Dilation, Rotation, Similar, Tessellation

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## References

Coxeter, H. S. M. and Greitzer, S. L. "Spiral Similarity." §4.8 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 95-100, 1967.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 239, 1991.

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Spiral Similarity

## Cite this as:

Weisstein, Eric W. "Spiral Similarity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpiralSimilarity.html