Every large point set has an obtuse angle

  • Martin Aigner
  • Günter M. Ziegler
Chapter

Abstract

Around 1950 Paul Erdős conjectured that every set of more than 2 d points in 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 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

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

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 1
  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany

Personalised recommendations