[math-fun] Dense unit distance graphs.
For a given set of k points in the plane, some number n of the mutual distances are 1. How big can we make n for a given k? A186705 at OEIS given the answers we know, but only up to 14 vertices. Where can I see pictures of example maximal unit distance graphs? The first "surprise" is a(9)=18; I would love to see that one.
From the last picture at https://math.stackexchange.com/questions/2575268/maximally-dense-unit-distan...
Points 4, 8, 7, 3, 10, 14, 9, 13, 5 I have them somewhere. There is a low-res image in Research Problems in Discrete Geometry by Brass Moser Pach. --Ed Pegg Jr On Mon, Sep 17, 2018 at 1:10 PM Allan Wechsler <acwacw@gmail.com> wrote:
For a given set of k points in the plane, some number n of the mutual distances are 1. How big can we make n for a given k? A186705 at OEIS given the answers we know, but only up to 14 vertices.
Where can I see pictures of example maximal unit distance graphs? The first "surprise" is a(9)=18; I would love to see that one. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Ooh, that is quite a lovely object. If I understand what I am seeing, there are six triangles, three red and three blue, arranged so that each of the nine red-blue pairs shares one vertex. It has one degree of freedom, right? I'd love to see a video of it "breathing". On Mon, Sep 17, 2018 at 2:23 PM Ed Pegg Jr <ed@mathpuzzle.com> wrote:
From the last picture at
https://math.stackexchange.com/questions/2575268/maximally-dense-unit-distan...
Points 4, 8, 7, 3, 10, 14, 9, 13, 5
I have them somewhere. There is a low-res image in Research Problems in Discrete Geometry by Brass Moser Pach.
--Ed Pegg Jr
On Mon, Sep 17, 2018 at 1:10 PM Allan Wechsler <acwacw@gmail.com> wrote:
For a given set of k points in the plane, some number n of the mutual distances are 1. How big can we make n for a given k? A186705 at OEIS given the answers we know, but only up to 14 vertices.
Where can I see pictures of example maximal unit distance graphs? The first "surprise" is a(9)=18; I would love to see that one. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Page 112 : http://cristal.univ-lille.fr/~jdelahay/pls/2014/252.pdf (for n=6, drawing 2, one segment is missing) JP Delahaye Le 17/09/2018 à 20:09, Allan Wechsler a écrit :
For a given set of k points in the plane, some number n of the mutual distances are 1. How big can we make n for a given k? A186705 at OEIS given the answers we know, but only up to 14 vertices.
Where can I see pictures of example maximal unit distance graphs? The first "surprise" is a(9)=18; I would love to see that one. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- ------------------------------------------------------------------- Jean-Paul DELAHAYE Professeur émérite, Université de Lille CRISTAL UMR CNRS 9189 (Centre de recherche en informatique, signal et automatique de Lille) Bat M3-Ext, Université de Lille 1, 59655, Villeneuve d'Ascq CEDEX France Portable : 06-30-71-08-95 E-mail : jean-paul.delahaye@univ-lille1.fr Page personnelle : http://cristal.univ-lille.fr/~jdelahay/ Blog : http://www.scilogs.fr/complexites/
participants (3)
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Allan Wechsler -
Ed Pegg Jr -
Jean-Paul Delahaye