The sphere packing problem

نویسنده

  • Thomas C. Hales
چکیده

Hales, T.C., The sphere packing problem, Journal of Computational and Applied Mathematics 44 (1992) 41-76. The sphere packing problem asks whether any packing of spheres of equal radius in three dimensions has density exceeding that of the face-centered-cubic lattice packing (of density IT/V%). This paper sketches a solution to this problem.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Sphere-Packing Problem

A brief report on recent work on the sphere-packing problem. 1991 Mathematics Subject Classification: 52C17

متن کامل

Local Covering Optimality of Lattices : Leech Lattice versus Root Lattice E 8

The Leech lattice is the exceptional lattice in dimension 24. Soon after its discovery by Leech [9], it was conjectured that it is extremal for several geometric problems in R: the kissing number problem, the sphere packing problem, and the sphere covering problem. In 1979, Odlyzko and Sloane and independently Levenshtein solved the kissing number problem in dimension 24 by showing that the Lee...

متن کامل

Serial Symmetrical Relocation Algorithm for the Equal Sphere Packing Problem

For dealing with the equal sphere packing problem, we propose a serial symmetrical relocation algorithm, which is effective in terms of the quality of the numerical results. We have densely packed up to 200 equal spheres in spherical container and up to 150 equal spheres in cube container. All results are rigorous because of a fake sphere trick. It was conjectured impossible to pack 68 equal sp...

متن کامل

New Upper Bounds on Sphere Packings I

We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.

متن کامل

1 O ct 2 00 1 NEW UPPER BOUNDS ON SPHERE PACKINGS

We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001