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# Every large point set has an obtuse angle

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## Abstract

Around 1950 Paul Erdős conjectured that every set of more than 2^{ d } points in *ℝ*^{ d } determines at least one obtuse angle, that is, an angle that is strictly greater than \(\frac{\pi}{2}\). In other words, any set of points in *ℝ*^{ d } which only has acute angles (including right angles) has size at most 2^{ d }. This problem was posed as a “prize question” by the Dutch Mathematical Society — but solutions were received only for *d* = 2 and for *d* = 3.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018