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Hilbert¡¯s 18th problem In 1900, David Hilbert presented to the International Mathematical Congress in Paris a list of 23 problems which he hoped would guide mathematical research in the twentieth century. The 18th problem was concerned with sphere packing and space-filling polyhedra. "I point out the following question (. . .) important to number theory and perhaps sometimes useful to physics and chemistry: How one can arrange most densely in space an infinite number of equal solids of given form, e.g., spheres with given radii or regular tetrahedra with given edges (or in prescribed positions), that is, how can one so fit them together that the ratio of the filled to the unfilled space may be as great as possible?" Õâ¸öÎÊÌâͨ³£½ÐKepler Conjecture¡£¾Ý˵×îÔçÊÇÒ»¸öº£µÁÌá³öÀ´µÄ£¬ËûÏëÖªµÀÄÜ·ñ²âÁ¿Ò»Ï¼װåÉÏÅÚµ¯£¨Ô²ÇòµÄ£©¶ÑµÄ´óС£¬¾ÍÖªµÀÂòÀ´Á˶àÉÙÅÚµ¯¡£ºóÀ´ÑÝ»¯³ÉÒ»¸öÊýѧÄÑÌâ¡£KeplerÍÆ¶Ï£¨1611Äê£©ÍÆ¶Ï×îÃܵĶѻý·½Ê½ÊÇÃæÐÄÁ¢·½£¨fcc£©£¬¶Ñ»ýÂÊΪ0.7404 . . . £¬µ«Ã»ÓÐÖ¤Ã÷¡£¾Ý˵ºóÀ´Óиö»ªÈ˸ø³öÁËÖ¤Ã÷£¬µ«ºÜ¿ì±»ÈËÕÒ³öÁË©¶´¡£ ×î½üÔÚ¿´¡¶The pursuit of perfect packing¡·Õâ±¾Ê飬ÀïÃæ¸ÕºÃÓÐÏà¹Ø½éÉÜ£¬ºÜ¿ÆÆÕ£¬ºÜÓÐȤ¡£ [ Last edited by attractor on 2010-1-7 at 22:11 ] |

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