3 research outputs found
Sets of points determining only acute angles and some related colouring problems
We present both probabilistic and constructive lower bounds on the maximum size of a set of points {S \subseteq \R^d} such that every angle determined by three points in {S} is acute, considering especially the case {S \subseteq \{0,1\}^d}. 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