[math-fun] Braced Heptagon
In Mathematica GraphData[{"UnitDistance", {21, 2}}] Is that a rigid graph? If so, it uses just 42 unit rods, beating the record at https://erich-friedman.github.io/mathmagic/0100.html
What version is needed? I've got Mathematica 11.3 and it says "no value associated with the specified arguments". On Fri, Dec 18, 2020, 23:22 ed pegg <ed@mathpuzzle.com> wrote:
In Mathematica GraphData[{"UnitDistance", {21, 2}}]
Is that a rigid graph? If so, it uses just 42 unit rods, beating the record at https://erich-friedman.github.io/mathmagic/0100.html
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Some code root=Root[1-8 #1+8 #1^2+6 #1^3-6 #1^4-#1^5+#1^6&,5];vals={{{7,0,0,0,0,0},{-41,72,12,-64,0,12}},{{49,-91,-14,77,0,-14},{1,-19,-2,13,0,-2}},{{28,-35,-7,35,0,-7},{20,-37,-5,29,0,-5}},{{0,0,0,0,0,0},{48,-72,-12,64,0,-12}},{{-28,35,7,-35,0,7},{20,-37,-5,29,0,-5}},{{-49,91,14,-77,0,14},{1,-19,-2,13,0,-2}},{{-7,0,0,0,0,0},{-41,72,12,-64,0,12}},{{13,-11,1,3,-1,0},{1,-7,-3,15,-1,-4}},{{5,-9,-2,7,1,-1},{-7,-5,-6,19,1,-5}},{{-3,28,-5,-24,3,5},{15,-32,9,12,-3,-1}},{{-10,-2,15,13,-5,-4},{2,-6,19,1,-5,0}},{{-9,3,-3,9,0,-3},{3,-1,1,-3,0,1}},{{-1,8,-21,5,5,-2},{-11,-4,17,7,-5,-2}},{{-7,13,-11,1,3,-1},{-5,-9,7,11,-3,-3}},{{0,23,1,-16,1,2},{4,-53,-7,36,1,-6}},{{-5,33,14,-24,-3,4},{-1,-43,6,28,-3,-4}},{{-3,57,6,-39,0,6},{-1,19,2,-13,0,2}},{{6,4,-9,-5,3,1},{-10,72,17,-47,-3,7}},{{13,-91,-11,62,1,-10},{9,-15,-3,10,1,-2}},{{-3,4,4,-7,-2,2},{7,-80,-12,59,2,-10}},{{2,-62,-9,43,2,-7},{2,-14,1,9,-2,-1}}}/4;unitlines={{1,2},{1,7},{1,9},{1,21},{2,3},{2,10},{2,15},{3,4},{3,11},{3,16},{4,5},{4,12},{4,17},{5,6},{5,13},{5,18},{6,7},{6,14},{6,19},{7,8},{7,20},{8,10},{8,13},{8,20},{9,11},{9,14},{9,21},{10,12},{10,15},{11,13},{11,16},{12,14},{12,17},{13,18},{14,19},{15,18},{15,19},{16,19},{16,20},{17,20},{17,21},{18,21}};pts=RootReduce[Map[Function[x,RootReduce[Sign[x.(root^Range[0,5])]Sqrt[Abs[x.(root^Range[0,5])]]]],vals,{2}]/Sqrt[7]];Graphics[{EdgeForm[{Black}],Table[Line[pts[[unitlines[[n]]]]],{n,1,42}],White,Table[Tooltip[{Disk[pts[[n]],.06],Black,Style[Text[n,pts[[n]]],8]},vals[[n]]],{n,1,Length[pts]}], Red, InfiniteLine[pts[[{1,18}]]]}] On Saturday, December 19, 2020, 10:20:02 AM CST, Hans Havermann <gladhobo@bell.net> wrote: It works in version 12.
On Dec 19, 2020, at 10:27 AM, William R Somsky <wrsomsky@gmail.com> wrote:
What version is needed? I've got Mathematica 11.3 and it says "no value associated with the specified arguments".
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I've convinced myself it is rigid. In fact, you can use three less struts and it remains rigid. (Just don't pull the wrong three struts! Take three of the four struts running to any one point and that point will swing free in the wind.) So if I've not made an error, the heptagon can be braced with 39 unit struts. I'm cleaning up my argument/proof at the moment and will make it available when that is done. On Sat, Dec 19, 2020, 08:20 Hans Havermann <gladhobo@bell.net> wrote:
It works in version 12.
On Dec 19, 2020, at 10:27 AM, William R Somsky <wrsomsky@gmail.com> wrote:
What version is needed? I've got Mathematica 11.3 and it says "no value associated with the specified arguments".
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William removed 2 vertices from my construction and lowered the heptagon bracing to 35 edges. https://math.stackexchange.com/questions/3954719/is-this-braced-heptagon-a-r... --Ed Pegg Jr On Sunday, December 20, 2020, 02:36:26 AM CST, William R Somsky <wrsomsky@gmail.com> wrote: I've convinced myself it is rigid. In fact, you can use three less struts and it remains rigid. (Just don't pull the wrong three struts! Take three of the four struts running to any one point and that point will swing free in the wind.) So if I've not made an error, the heptagon can be braced with 39 unit struts. I'm cleaning up my argument/proof at the moment and will make it available when that is done. On Sat, Dec 19, 2020, 08:20 Hans Havermann <gladhobo@bell.net> wrote:
It works in version 12.
On Dec 19, 2020, at 10:27 AM, William R Somsky <wrsomsky@gmail.com> wrote:
What version is needed? I've got Mathematica 11.3 and it says "no value associated with the specified arguments".
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participants (3)
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ed pegg -
Hans Havermann -
William R Somsky