Affine contractions on the plane
INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, cilt.38, sa.5, ss.701-707, 2007 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 5
- Basım Tarihi: 2007
- Doi Numarası: 10.1080/00207390701368587
- Dergi Adı: INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.701-707
- Anadolu Üniversitesi Adresli: Evet
Özet
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.