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Paterson, Michael S., Peres, Y., Thorup, Mikkel, Winkler, P. and Zwick, Uri (2009) Maximum overhang. American Mathematical Monthly, Vol.116 (No.9). pp. 765-787. doi:10.4169/000298909x474855 ISSN 0002-9890.
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Official URL: http://www.maa.org/pubs/monthly.html
Abstract
A 150-year-old problem asks how many identical rectangular blocks of length 1, balanced at the edge of a table, are needed to achieve some given overhang D beyond the table edge. A well-known construction based on the harmonic series requires a number of blocks which grows exponentially with D. Many people had assumed that this was optimal until a construction by Paterson and Zwick in this MONTHLY (January 2009) showed that a quantity just cubic in D was sufficient. The current paper settles this classic problem within a constant factor, proving cubic growth to be not only sufficient, but also necessary.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Logarithms | ||||
| Journal or Publication Title: | American Mathematical Monthly | ||||
| Publisher: | Mathematical Association of America | ||||
| ISSN: | 0002-9890 | ||||
| Official Date: | November 2009 | ||||
| Dates: |
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| Volume: | Vol.116 | ||||
| Number: | No.9 | ||||
| Number of Pages: | 26 | ||||
| Page Range: | pp. 765-787 | ||||
| DOI: | 10.4169/000298909x474855 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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