Abstract
Assume that T_h is a triangle with the interior angles at the base of the measure not greater than 90^0, with the base length 1 and the height h. Let S be a square with a side parallel to the base of T_h and let {S_n} be a collection of the homothetic copies of S. A tight upper bound of the sum of the areas of squares from {S_n} that can be parallel packed into a triangle T_h is determined.
Highlights
Let P be a polygon and let Si be a square for i = 1, 2, . . . One side of P is called the base of P
A collection S1, S2, . . . is said to be packed into P if their union is contained in P and if these squares have pairwise disjoint interiors
Assume that S is a square and that Th is a triangle with the interior angles at the base of the measure not greater than 90◦, with the base length 1 and the height h
Summary
Let P be a polygon and let Si be a square for i = 1, 2, . Is said to be packed into P if their union is contained in P and if these squares have pairwise disjoint interiors. A packing is called parallel if a side of each packed square is parallel to the base of P. The goal is to pack the squares into P with high density. Let (P ) be the greatest number such that any collection of squares of the total area not greater than (P )·|P | can be parallel packed into P. Assume that S is a square and that Th is a triangle with the interior angles at the base of the measure not greater than 90◦, with the base length 1 and the height h.
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