RETRACTED: Characterization of Pythagorean curves and Pythagoreanization using a rational transform

This article has been retracted at the request of the Editor-in-Chief and the authors. Reason: it has been found belatedly that the main result of the paper is not original to their research (see the authorsʹ statement below). We, the editors, apologize to the readers for any confusion and we will make every effort to prevent such a regrettable case in future. In this effort, we also sincerely remind authors of their scientific duty to carry out a complete literature search before making originality claims in submitted articles. Authorsʹ Statement: “We, the authors of the article, ‘Characterization of Pythagorean curves and Pythagoreanization using a rational transform’, Journal of Symbolic Computation 37 (2004), 377–389, were alerted by Professor RidaFarouki that the result presented in the article may have been previously obtained by Dr. Wei Lü in the article, ‘Offset-rational parametric plane curves’, Computer Aided Geometric Design 12 (1995), 601–616. We have checked it. Even though there are some differences, we agree that Wei Lü indeed has a precedence on the main result and thus he should be given the full credit on the result. Accordingly, we also agree with the editorʹs decision to retract the article. We regret that we have not carried out a complete literature search before embarking on our work. We apologize to Dr. Wei Lü and colleagues for any confusion caused by our mistake. We have learned the importance of a complete literature search. Most of all, we thank Professor RidaFarouki for kindly alerting us to the problem.” Min-Ho Ahn and Gwang-Il Kim