[seqfan] Re: Number of touching points between unit circles in the optimal packing of circles in a circle
Benoît Jubin
benoit.jubin at gmail.com
Sun Mar 19 15:30:41 CET 2017
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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