Packing a rectangle with m × (m + 1) rectangles

摘要

We consider the packing of rectangles of dimension m × (m + 1) -where m is a natural number - into a larger rectangle. More specifically, we consider the following problem: What is the smallest area of a rectangle into which rectangles of dimensions 1 × 2, 2 × 3, 3 × 4,..., n × (n + 1) will fit without overlap?