Parallel Packing Squares into a Triangle

Abstract

AbstractAssume that$$T_h$$This a triangle with the interior angles at the base of the measure not greater than$$90^0$$900, with the base length 1 and the heighth. LetSbe a square with a side parallel to the base of$$T_h$$Thand let$$\{S_n\}$${Sn}be a collection of the homothetic copies ofS. A tight upper bound of the sum of the areas of squares from$$\{S_n\}$${Sn}that can be parallel packed into a triangle$$T_h$$This determined.