# Tagged Questions

**7**

votes

**1**answer

190 views

### For a 3D Apollonian packing, do we really know that the Hausdorff dimension of the complement is approximated by the growth rate of curvature?

The fractal dimension of the 3D Apollonian packing is computed in this paper.
In the introduction, the authors cite three of Boyd's paper (Ref 2, 5, 6) to support that the fractal dimension ...

**5**

votes

**0**answers

385 views

### N-balls covering n-balls

This question is a follow-on question from:
Covering a unit ball with balls half the radius
The questions are these:
Given an arbitrary dimension d, and a unit n-ball in d-dimensional Euclidean ...

**9**

votes

**4**answers

737 views

### Optimal pebble-packing shape

Suppose you throw many ($n$) congruent convex bodies (in $\mathbb{R}^3$) of unit volume (or of unit area in $\mathbb{R}^2$) into a large container, and shake it until little else changes.
Q. ...

**34**

votes

**6**answers

992 views

### Tetris-like falling sticky disks

Suppose unit-radius disks fall vertically from $y=+\infty$,
one by one, and create a random jumble of disks above the $x$-axis.
When a falling disk hits another, it stops and sticks there.
Otherwise, ...

**20**

votes

**6**answers

2k views

### Covering a unit ball with balls half the radius

This is a direct (and obvious) generalization of the recent MO question, "Covering disks with smaller disks":
How many balls of radius $\frac{1}{2}$ are needed to cover completely a ball of radius ...

**8**

votes

**5**answers

740 views

### Extensions of the Koebe–Andreev–Thurston theorem to sphere packing?

The Koebe–Andreev–Thurston theorem states that any planar graph can be represented
"in such a way that its vertices correspond to disjoint disks, which touch if and only if
the corresponding vertices ...

**12**

votes

**2**answers

663 views

### Average degree of contact graph for balls in a box

Imagine you dump congruent, hard, frictionless balls in a box,
letting gravity compress the balls into a stable configuration
(I believe such configurations are called
jammed.)
Assume the box ...