کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4582378 1333795 2014 68 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Packing, covering and tiling in two-dimensional spaces
ترجمه فارسی عنوان
بسته بندی، پوشش و کاشی کاری در فضاهای دو بعدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Packing, covering and tiling is a fascinating subject in pure mathematics. It mainly deals with arrangement patterns and efficiencies of geometric objects. This subject has a long and rich history, even back to Kepler, Newton, Lagrange and Gauss. Inspired by its applications and with the help of computing methods, in recent years it has become a very active research area in mathematics once again. Most of the fundamental problems in this subject can be characterized as simple sounding but challenging. This subject has important applications in many other areas such as Number Theory, Logic, Complex Analysis, Optimization, Coding Theory, Crystallography, Material Science, Industry, and even Biology. In spite of the long history, many of its key problems are still open, even in the plane. The purpose of this paper is to present a comprehensive review for packing, covering and tiling in the two-dimensional spaces. We will focus on the key problems, the fundamental results, the creative ideas, some important applications, and some significant connections with other areas.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Expositiones Mathematicae - Volume 32, Issue 4, 2014, Pages 297–364
نویسندگان
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