Re: Circles packed within a circle.
From: David W. Cantrell (DWCantrell_at_sigmaxi.org)
Date: 10/28/04
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Date: 28 Oct 2004 13:21:57 GMT
w.taylor@math.canterbury.ac.nz (Bill Taylor) wrote:
> This must surely be well studied already?
>
> It is desired to pack as many unit circles within a circle radius R >1 .
> Non-overlapping of course, though they may be tangential.
>
> Clearly for R < 2, only one circle will fit.
>
> For R >=2, but less than some larger easily-calulable number,
> 2 circles is OK, but for R >= this, one can fit 3.
>
> Similarly one may get 4 at some higher number; then 5.
>
> BUT NOT 6 !
> As soon as it becomes possible to fit six circles inside, it is already
> possible to fit seven! There is no maximal pattern of six circles.
>
> There are certain other numbers of circles which cannot be maximal
> numbers.
18 is surely such a number. But what makes you think that there need be any
other such numbers? I think, offhand, that there might not be any others.
> What is known about this in general?
I don't know. Look at
<http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html> and find N such
that the radius is the same as for N+1.
Cheers,
David
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