Affine contractions on the plane

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Copy For Citation

Celik D., Ozdemir Y., Ureyen M.

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, vol.38, no.5, pp.701-707, 2007 (ESCI)

• Publication Type: Article / Article
• Volume: 38 Issue: 5
• Publication Date: 2007
• Doi Number: 10.1080/00207390701368587
• Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
• Page Numbers: pp.701-707
• Anadolu University Affiliated: Yes

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.