On packing squares with equal squares (Q1224588)

Let \(\alpha\) be a positive real number. Let \(N(\alpha)\) denote the maximum number of nonoverlapping open unit squares that can be packed into a square of side \(\alpha\). By a clever construction it is shown that \(\alpha ^2-N(\alpha)=0(\alpha ^{7/11})\). The authors raise a number of related questions.