Optimal block stacking and combinatorial identities via Archimedes' method

2018-01-16T03:17:15Z (GMT) by DAVID TREEBY
What is the maximum overhang that can be obtained when a set of blocks of variable width are stacked so that there is one block at each level? We determine the configuration of blocks that maximises the overhang when these blocks are stacked in a prescribed order. We also describe infinite sets of blocks of variable width that can be stacked to yield towers with arbitrarily large overhang. Additionally, we consider various symmetric configurations of blocks and point masses in the plane. By considering the centres of mass of such configurations we establish various well-known summation formulas, and discover others that are new and appealing.