# Maximum overhang

- Published in 2007
- Added on

In the collections

How far can a stack of $n$ identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order $\log n$. Recently, Paterson and Zwick constructed $n$-block stacks with overhangs of order $n^{1/3}$, exponentially better than previously thought possible. We show here that order $n^{1/3}$ is indeed best possible, resolving the long-standing overhang problem up to a constant factor.

## Links

## Other information

- key
- Maximumoverhang
- type
- article
- date_added
- 2021-03-15
- date_published
- 2007-07-24

### BibTeX entry

@article{Maximumoverhang, key = {Maximumoverhang}, type = {article}, title = {Maximum overhang}, author = {Mike Paterson and Yuval Peres and Mikkel Thorup and Peter Winkler and Uri Zwick}, abstract = {How far can a stack of {\$}n{\$} identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order {\$}\log n{\$}. Recently, Paterson and Zwick constructed {\$}n{\$}-block stacks with overhangs of order {\$}n^{\{}1/3{\}}{\$}, exponentially better than previously thought possible. We show here that order {\$}n^{\{}1/3{\}}{\$} is indeed best possible, resolving the long-standing overhang problem up to a constant factor.}, comment = {}, date_added = {2021-03-15}, date_published = {2007-07-24}, urls = {http://arxiv.org/abs/0707.0093v1,http://arxiv.org/pdf/0707.0093v1}, collections = {basically-physics,easily-explained,fun-maths-facts,puzzles}, url = {http://arxiv.org/abs/0707.0093v1 http://arxiv.org/pdf/0707.0093v1}, year = 2007, urldate = {2021-03-15}, archivePrefix = {arXiv}, eprint = {0707.0093}, primaryClass = {math.HO} }