All Questions

There is a lot of interest in the maximal density of equal circle packing in a circle. And I thought that knowing whether or not the solution is always algebraic or not would be useful. My original ...

We try to add to A Variant of the Malfatti Problem As stated in the Wikipedia entry on Malfatti circles, it is an open problem to decide, given a number $n$ and any triangle, whether a greedy method ...

Packing problems often ask for the largest number of some identical shape that can fit in a given space without overlapping, if they are placed optimally. I'm interested in the opposite question: Q. ...

This is a cross-post. Let $(a_n)_{n \in \mathbb{Z}}$ be some given, strictly increasing sequence of positive numbers, such that $\lim_{n \to -\infty} a_n=0,\lim_{n \to +\infty} a_n=+\infty$. Let $\...

The problem of the expected density of a saturated random packing of unit circles in the plane can be described as follows. In a circular region $C$ of a large radius pick a point at random and draw ...

I need to create about 100 (small) holes in a distributor plate (hole diam = 0.5 mm; plate diameter = 100 mm). The sm. holes should be distributed in such a way that the density (hole/area) is nearly ...