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  5. Construction of initial points for decision of task of packing of congruent balls in ball

Construction of initial points for decision of task of packing of congruent balls in ball

G.N. Yas'kov
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The paper considers the problem of packing congruent solid spheres of given radius into a ball of larger radius. A mathematical model of the problem based on increasing the number of variables is given and its basic properties are described. Three different ways to construct the starting points are constructed. With a large number of spheres, starting points are established in accordance with the lattice packing of spheres. Described are two ways of constructing the initial points that use a lattice packing. The third method of constructing the initial points is based on random choice and can be used when a small number of balls is given.
Keywords: packing, ball, mathematical model, hexagonal grate, initial point