---

Statement

Conjecture (p. 54, quoted). "Given $2^n+1$ points in $n$-space, there is an angle determined by these points which is greater than $\frac12\pi$."

The paper attributes it to P. Erdős, calls the case $n=2$ trivial, credits $n=3$ to N. H. Kuiper and A. H. Boerdijk (unpublished, footnote 2), says the answer is unknown for $n>3$, and adds that the method of Section 4 seems not to apply. A footnote added in proof (p. 54) records that the conjecture had recently been proved by Danzer and Grünbaum, "in a surprisingly simplex [sic] way".

Scope

A conjecture the paper records, with a report of its proof; the paper proves nothing about it and cites no publication for the Danzer--Grünbaum proof.

Read depth. Claims checked: the sentence, footnote 2 and the footnote added in proof were read on p. 54 of the print.

Source. P. Erdős and G. Szekeres, On some extremum problems in elementary geometry, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 3--4 (1960/1961), 53--62; the edition read is named on the source card.

Bears on

• Problem 224: the conjecture is the problem's statement in dimension $n$, with "obtuse" read as greater than $\pi/2$; the paper reports Danzer and Grünbaum's proof without giving it.