Magic Hexagram

Author

Eric W. Weisstein
February 9, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/RecreationalMath/MagicHexagram.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MagicHexagram.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Figure

<<Graphics`Arrow`

ClosedLine[l_List?MatrixQ]:=Line[Append[l,First[l]]]

LinedHexagram={ClosedLine/@Transpose[Partition[Through[{Sin,Cos}[Pi #/3]]&/@Range[0,5],2]],
Hexagram,
Line/@Transpose[Partition[Through[{Cos,Sin}[Pi #/3]]&/@Range[0,5],3]/Sqrt[3]]};

Show[Graphics[
{
LinedHexagram,
Map[Arrow@@#&,Table[{{Cos[t],Sin[t]},{-Sin[t],Cos[t]}}.#&/@{{-1.5,.25#},{-1,.25#}}&/@{-1,1},{t,0,2Pi/3,Pi/3}],{2}]
}
],AspectRatio->Automatic]

Numbers[l_List]:=Text@@@Transpose[{Flatten[l],Join@@(Through[{Sin,Cos}[-Pi #/3]]&/@Range[0,5]#&/@{.35,.67})}]

Show[GraphicsArray[Graphics[{LinedHexagram,Numbers[#]},AspectRatio->Automatic]&/@
{
{{9,12,3,5,7,6},{1,2,8,11,10,4}},
13-{{9,12,3,5,7,6},{1,2,8,11,10,4}}
}
]]