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Affine contractions on the plane

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Abstract:

Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians. Then, a sufficient condition is given for such a transformation to be a contraction.

Document Type: Research Article

DOI: https://doi.org/10.1080/00207390701368587

Publication date: 2007-01-01

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