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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metric
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 Δ be an arbitrary triangle with minimum angle α. Let Δ′ be any triangle generated in the iterated application of the longest-edge trisection. Let α′ be the minimum angle of Δ′. Thus α′⩾α/c with c=π/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
نویسندگان
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