Problem 352

Erdős Problem #352: declared status 'open'. Formalized: yes. Is there some $c>0$ such that every measurable $A\subseteq \mathbb{R}^2$ of measure $\geq c$ contains the vertices of a triangle of area 1? Current best: In [Er78d] and [Er83d] he speculated that perhaps $C=4\pi/\sqrt{27}\approx 2.418$ works, which would be the best possible, as witnessed by a circle of radius $<2\cdot 3^{-3/4}$. Freiling and Mauldin (see [Ma13]) have proved this conjecture if $1\leq n\leq 3$. Prize: no. Tags: geometry.