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Published in:
2004 | OriginalPaper | Chapter
Every large point set has an obtuse angle
Authors : Martin Aigner, Günter M. Ziegler
Published in: Proofs from THE BOOK
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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Around 1950 Paul Erdös conjectured that every set of more than 2dpoints in ℝd 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 ℝdwhich only has acute angles (including right angles) has size at most 2d. 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.