Overhang

Details Overhang Overhang

2007-10-12

arxiv.org/abs/0710.2357v1

Mathematics

History and Overview

27 pages, 24 figures. To appear in American Mathematical Monthly

Scientific paper

How far off the edge of the table can we reach by stacking $n$ identical, homogeneous, frictionless blocks of length 1? A classical solution achieves an overhang of $1/2 H_n$, where $H_n ~ \ln n$ is the $n$th harmonic number. This solution is widely believed to be optimal. We show, however, that it is, in fact, exponentially far from optimality by constructing simple $n$-block stacks that achieve an overhang of $c n^{1/3}$, for some constant $c>0$.

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