All Questions

The greedy circle packing of a bounded region in the plane is the result of placing at each stage the largest possible disk into the region that remains uncovered. The greedy circle packing of a ...

I posted this question many years ago on math stackexchange but it did not get an answer. It had circulated as a puzzle in graduate school. A disk $D$ of radius $1$ contains disks $D_i$ ($i \ge 1$) of ...

Since 2013, I found Some problems on Apollonian Gasket as following. These problem also is higher level of Eppstein Point. I am looking for a proof of one of these problems: Let three $(A)$, $(B)$, $(...

By my computation, I pose a conjecture as follows and I am looking for a proof: Conjecture: Let $(O)$ be a circle with radius $R$, and $n$ be positive integer $n\ge 3$. Construct $n$ circles $(...

Consider firewood logs as unit-radius cylinders of the same length. Each log is split into $k$ pieces by equiangular sectors meeting in the circle center: $k=2$ leads to semicircles, $180^\circ$; $k=3$...

By using a regular hexagonal arrangement it is simple to fit 19 identical circles into a larger circle of five times the radius with no circles overlapping. This leaves an area equal to six smaller ...