کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6421469 | 1631833 | 2013 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metric
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
From an initial triangle, three triangles are obtained joining the two equally spaced points of the longest-edge with the opposite vertex. This construction is the base of the longest-edge trisection method. Let Î be an arbitrary triangle with minimum angle α. Let Îâ² be any triangle generated in the iterated application of the longest-edge trisection. Let αⲠbe the minimum angle of Îâ². Thus αâ²â©¾Î±/c with c=Ï/3arctan3/11 is proved in this paper. A region of the complex half-plane, endowed with the Poincare hyperbolic metric, is used as the space of triangular shapes. The metric properties of the piecewise-smooth complex dynamic defined by the longest-edge trisection are studied. This allows us to obtain the value c.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 221, 15 September 2013, Pages 424-432
Journal: Applied Mathematics and Computation - Volume 221, 15 September 2013, Pages 424-432
نویسندگان
Francisco Perdomo, Ángel Plaza,