By Walter E. Meyerhof

For undergraduate physics scholars or for nuclear engineers.

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To this we might add a verse to bring it up to date: If you fail to reach your end, your siege has come to nought, call on your electronic friend, to spare a microsecond’s thought. Whether computers can really ‘think’ is a deeper problem than the merely technical one of proof-checking. We may someday accept an even stranger role for these machines in mathematics. Will they write books as well? ¾ For a further exploration of this ongoing debate, see the article by: Horgan J 1993 The death of proof Sci.

Many loose crystalline packings have been proposed. For instance, ¼ ½¾¿ . 4(b)) was obtained sphere packing. Recently a packing with by decorating, with tetrahedra, the vertices of the CdSO net10 . 11 The lowest known density for stable packing is ¼¼ . This value is about ten times smaller than the one for the loose random packing. 4 are highly symmetric and cannot be obtained or approximated by simply mixing spheres at random. 7 Ordered close packing What about dense ordered packings of spheres, the central question, from which we have digressed?

Occasionally, when it is not been allowed enough time to settle, the cement behaves in a much more fluid manner. A disaster ensues when the hopper is opened9. 6 Ordered loose packings Ordered loose packings sometimes occur in the study of crystal structures. Here our question may be turned on its head: what is the lowest possible density for a packing of hard spheres which is still mechanically stable or ‘rigid’? For such rigidity, each sphere needs at least four contacts and these cannot be all in the same hemisphere.