On the cardinality of sets in ${\bf R}^d$ obeying a (possibly slightly obtuse) angle bound
2020
In this paper we explicitly estimate the number of points in a subset $A
\subset {\bf R}^{d}$ as a function of the maximum angle $\angle A$ that any
three of these points form, provided $\angle A < \theta_d := \arccos(-\frac 1
{d}) \in (\pi/2,\pi)$. We also show $\angle A < \theta_d$ ensures that $A$
coincides with the vertex set of a convex polytope. This study is motivated by
a question of Paul Erd\"os and indirectly by a conjecture of L\'aszl\'o Fejes
T\'oth.
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