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We present both probabilistic and constructive lower bounds on the maximum size of a set of points such that every angle determined by three points in is acute, considering especially the case . These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.
|Item Type:||Journal Article|
|Copyright Holders:||2006 David Bevan|
|Academic Unit/Department:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||David Bevan|
|Date Deposited:||31 May 2012 08:46|
|Last Modified:||02 Aug 2016 21:21|
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