Re: Circles packed within a circle.
From: HP (yae9911_at_netscape.net)
Date: 10/28/04
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Date: 28 Oct 2004 08:16:43 -0700
w.taylor@math.canterbury.ac.nz (Bill Taylor) wrote in message news:<716e06f5.0410272054.2cd4b912@posting.google.com>...
> 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.
>
>
> What is known about this in general?
>
> ------------------------------------------------------------------------------
> Bill Taylor W.Taylor@math.canterbury.ac.nz
> ------------------------------------------------------------------------------
The most comprehensive archive of solutions can be found at E. Specht's
"The best known packings of equal circles in the unit circle (up to N = 500)"
http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html with links to pictures e.g.
http://hydra.nat.uni-magdeburg.de/packing/cci/cci17.html
Hugo Pfoertner
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