ON CLOSE PACKING OF SOLIDS IN THREE-DIMENSIONAL SPACE
Romanov Vadim Nikolaevich
Saint-Petersburg
Abstract. The article gives a solution for the task of the close packing of solids of different shapes in three-dimensional Euclidean space. As the standards of comparison the author considers solids forming a partition of three-dimensional space, namely, hexahedron, rectangular prism, triangular prism, hexagonal prism. The dependence on the choice of the standard of relative volume and filling factor for a number of solids, in particular, solids of revolution and regular polyhedrons is studied. The paper also proposes an algorithm for the solution of the task for bodies of arbitrary shape depending on topological properties and smoothness.
Key words and phrases: теория чисел, плотная упаковка, эталон, тела вращения, правильные многогранники, относительный объем, коэффициент заполнения, theory of numbers, close packing, standard, solids of revolution, regular polyhedrons, relative volume, filling factor
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Korn G., Korn T. Spravochnik po matematike. M.: Nauka, 1973. 832 s.
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Gil'bert D. Izbrannye trudy. M.: Faktorial, 1998. T. 2. Analiz. Fizika. Problemy. 608 s.
Korn G., Korn T. Spravochnik po matematike. M.: Nauka, 1973. 832 s.
Kurant R., Gil'bert D. Uravneniya s chastnymi proizvodnymi. M.: Mir, 1964. 830 s.
Русский
