[seqfan] Re: How many squares can you make from n points in the plane?
njasloane at gmail.com
Fri Oct 1 02:45:44 CEST 2021
Benoit, There have been so many new developments (they are all in this
email thread, though), that I have lost track of where we are.
But you seem to be on top of things. Could I ask you to edit the entry,
and bring it up to date?
I'll send you the text file of the a(7) = 3 proof, in case it will be
Neil J. A. Sloane, Chairman, 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 Thu, Sep 30, 2021 at 6:42 PM Benoît Jubin <benoit.jubin at gmail.com> wrote:
> On Thu, Sep 30, 2021 at 10:01 PM Frank Adams-watters via SeqFan
> <seqfan at list.seqfan.eu> wrote:
> > Does this actually get us any new values? I.e., min = max.
> Apparently it does not. So far, we have exact values (for both a(n)
> and b(n)) for n up to 9, thanks to Sascha.
> Peter's configurations are clever. They made me think of two things:
> * An interesting representation of a configuration is an integer
> matrix where integers represent the number of squares a given vertex
> belongs to. For instance:
> optimal 6-configurations:
> optimal 9-configuration:
> * The "asymptotic solution" is not the full [1,sqrt(n)]^2 grid but may
> be the full disc of radius sqrt(n/pi).
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