5 problems

A nonnegative integer $n$ is maximally circlable if there exists a largest circle enclosing exactly $n$ lattice points in its interior; otherwise it is non-maximally circlable. Inf…

Let $n\in\mathbb{N}$ be a centred hexagonal number, and consider the smallest hexagon containing $n$ disks and the smallest hexagon containing $n-1$ disks. Centred-hexagonal-number…

Let $n>3$ be a triangular number, and consider the smallest triangle containing $n$ disks and the smallest triangle containing $n-1$ disks. Erdős–Oler-type conjecture. The smallest…

Let $n$ unit disks be given, and let $m$ be a positive integer such that … The smallest triangle containing these disks is an equilateral triangle of side length $2(m-1)+2\sqrt{3}$…

Let $G_n$ be a random triangulation with $n$ vertices, and consider its circle packing, or another natural embedding, in the unit sphere. Let $\mu_n$ be the random measure on the s…