# Tag Info

Accepted

• 85.2k

### Density of a saturated random packing of congruent circles

Following user @j.c.'s lead, here is another paper on RSA (Random Sequential Adsorption), which concludes with a density of $0.77$. From the abstract: Hinrichsen, Einar L., Jens Feder, and Torstein ...
• 150k
Accepted

### Squaring a square and discrete Ricci flow

My question is answered in Lovász's book: Lovász, László. Graphs and Geometry. Vol. 65. American Mathematical Soc., 2019. p.82: Theorem 6.2. Every planar map in which the unbounded country is a ...

### Squaring a square and discrete Ricci flow

I just found this citation, not cited in the AMS Notices paper (but I cannot yet access the Israel J Math paper itself): Schramm, Oded. "Square tilings with prescribed combinatorics." ...

### Squaring a square and discrete Ricci flow

I don't know about having one vertex per square, but there is a similar very interesting construction with edges at squares. It does not answer your question but it will still surely interest you. ...
• 3,084

### The problem of finding the smallest number of copies of a certain shape that can be placed into a space to make fitting another copy impossible

On the sphere and for disks of radius $r$, your problem is equivalent to a covering problem with disks of radius $2r$. Given a collection of $k$ centerpoints of open $r$-disks on the sphere, you can ...
• 4,159

### Can we almost cover any shape in the plane by disjoint/tangent disks of prescribed radii?

There is a stronger result. Suppose that $(b_n)$ is a sequence with the properties $b_n>0,\; b_n\to 0$ and $\sum b_n^2=\infty$. Then for any region $D$, and for every $\epsilon>0$ there are ...
• 90.1k
Accepted

• 16.3k
1 vote
Accepted

### On covering a disk by non-overlapping subdisks

Proven by O. Wesler, “An infinite packing theorem for spheres,” PAMS Vol. 11, pp. 324-326, (1960).
• 2,274

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