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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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