Parallel packing and covering of an equilateral triangle with sequences of squares (Q987593)

Let \(T_e\) a triangle of unit sides. The author proves two theorems. Theorem 1. Any (finite or infinite) sequence of squares permits a parallel covering of \(T_e\) provided the total area of the squares is not smaller than 1.5. Theorem 2. Any (finite or infinite) sequence of squares can be parallel packed into \(T_e\) provided the total area of the squares does not exceed \(\frac 34 (2-\sqrt{3}\,)\).