All Questions
Tagged with circle-packing plane-geometry
6 questions
22
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Does greedy circle packing exhaust the measure of every bounded open set in the plane?
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 ...
7
votes
1
answer
225
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Optimal stacking of split logs
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, $180^\circ$;
$k=3$...
2
votes
1
answer
230
views
Some inequalities on chain of circle packing
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 $(...
2
votes
1
answer
127
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On covering a disk by non-overlapping subdisks
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 ...
1
vote
1
answer
322
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Settling a circular argument: room for one more?
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 ...
1
vote
0
answers
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Some Problems On Apollonian Gasket
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 $(A)$, $(B)$, $(...