کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425647 1633828 2014 61 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the translative packing densities of tetrahedra and cuboctahedra
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On the translative packing densities of tetrahedra and cuboctahedra
چکیده انگلیسی

In 1900, as a part of his 18th problem, Hilbert asked the question to determine the density of the densest tetrahedron packings. However, up to now no mathematician knows the density δt(T) of the densest translative tetrahedron packings and the density δc(T) of the densest congruent tetrahedron packings. This paper presents a local method to estimate the density of the densest translative packings of a general convex solid. As an application, we obtain the upper bound in0.3673469⋯≤δt(T)≤0.3840610⋯, where the lower bound was established by Groemer in 1962, which corrected a mistake of Minkowski. For the density δt(C) of the densest translative cuboctahedron packings, we obtain the upper bound in0.9183673⋯≤δt(C)≤0.9601527⋯. In both cases we conjecture the lower bounds to be the correct answer.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 260, 1 August 2014, Pages 130-190
نویسندگان
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