[seqfan] Re: Number of touching points between unit circles in the optimal packing of circles in a circle
Neil Sloane
njasloane at gmail.com
Sun Mar 19 15:58:57 CET 2017
The Wikipedia page only say that the circumradius has been
proved to be optimal (for n <= 13 circles)
It does NOT say that the total number of contacts
is optimal.
It would seem to me to be equally interesting to maximize
the number of pairwise contacts (B.J. suggested
minimizing them). We should probably have both
sequences - but only as far as they have been proved to be optimal.
Best regards
Neil
Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
On Sun, Mar 19, 2017 at 10:30 AM, Benoît Jubin <benoit.jubin at gmail.com> wrote:
> For a given n (number of disjoint unit disks), there can be many
> configurations acheiving the minimum r (smallest radius of an
> enclosing circle) with different t's (tangency numbers). You could
> define a(n) to be the minimal t among the optimal configurations.
>
> This reminds me of the "kissing numbers", which should be in the OEIS.
>
> Regards,
> Benoit
>
> On Sun, Mar 19, 2017 at 10:48 AM, Felix Fröhlich <felix.froe at gmail.com> wrote:
>> Dear Sequence Fans,
>>
>> Let A be an arrangement of n unit circles in the plane, let r the radius of
>> the smallest circle that can enclose A and let t be the number of points
>> where two unit circles in the arrangement touch each other.
>>
>> A sequence arising from the above is the following:
>>
>> a(n) = the value of t for the specific A such that r is minimal over all
>> possible A.
>>
>> https://en.wikipedia.org/wiki/Circle_packing_in_a_circle seems to suggest
>> that the sequence with offset 2 starts
>>
>> 1, 3, 4, 5, 6, 12, 7, 8, 12, 14
>>
>> This is not in the OEIS. Are the terms correct and should this be in the
>> OEIS?
>>
>> Best regards
>> Felix Fröhlich
>>
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