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?