2004 | OriginalPaper | Buchkapitel
Every large point set has an obtuse angle
verfasst von : Martin Aigner, Günter M. Ziegler
Erschienen in: Proofs from THE BOOK
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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.