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Prime Rotating Diagram

  • To: mathgroup at smc.vnet.net
  • Subject: [mg107002] Prime Rotating Diagram
  • From: a boy <a.dozy.boy at gmail.com>
  • Date: Sun, 31 Jan 2010 05:57:26 -0500 (EST)
  • References: <c724ed861001302150k5ada54e4j955b4ce6ad1d2374@mail.gmail.com>

PrimeRotatingDiagram.nb <http://att.newsmth.net/att.php?p.749.82091.545.nb>
- http://att.newsmth.net/att.php?p.749.82091.545.nb


     Suppose p[i] is the i-th prime. Start from coordinate origin (0,0)
 , firstly draw a line segment at the direction of positive X-axes and
 the length is 2=p[1], secondly rotate anticlockwise angle \[Theta] and
 draw a line segment lengthed 3=p[2], ... at the i-th step, rotate
 anticlockwise angle \[Theta] and draw a line segment lengthed p[i]...
 This is Prime Rotating Diagram G(\[Theta],p[n]).

 Block[{$RecursionLimit = 10000}, t
    \[Theta] = 1.01 Pi/2;
  n = 300;
  point[0] = {0, 0};
  point[i_Integer] :=
   point[i - 1] +
    Prime[i] {Cos[(i - 1) \[Theta]], Sin[(i - 1) \[Theta]]};
  Graphics[{Blue, Line[Table[point[i], {i, 1, n}]], Red,
    Circle[{0, 0}, 1]}, Axes -> True]
  ]
 (*Manipulate[Graphics[{Green,Line[Table[point[i],{i,1,n}]],Blue,Line[{\
 {0,0},{point[n][[1]],point[n][[1]]}}]},Axes->True],{n,1,1000}]*)

 For any G(\[Theta],p[n]), there is a minimal circle covering the diagram.

 I have some questions in the notebook in the link above.
Can you give me the answer or some advice, if you are in your free time?



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