Maximum overhang

• Published in 2007
• Added on 2021-03-15

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

• http://arxiv.org/abs/0707.0093v1
• http://arxiv.org/pdf/0707.0093v1

Other information

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 = {2007-10-09},
	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}
}