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Ultimately the goal is to make a manipulate command and turn a line into a circle.

So I am supposed to take a line that is segmented into 12 equal lengths.

M = {{1, 0}, {2, 0}, {3, 0}, {4, 0}, {5, 0}, {6, 0}, {7, 0}, {8, 
0}, {9, 0}, {10, 0}, {11, 0}, {12, 0}, {13, 0}};
Graphics[{Thin, 
Line[M, VertexColors -> {Red, Blue, Orange, Green, Red, Blue, 
 Orange, Green, Red, Blue, Orange, Green}]}]

Then there is the circle

L = {{1, 0}, {Cos[Pi/6], Sin[Pi/6]}, {Cos[(2 Pi)/6], 
Sin[(2 Pi)/6]}, {0, Sin[Pi/2]},  {-Cos[(2 Pi)/6], 
Sin[(2 Pi)/6]}, {-Cos[Pi/6], Sin[Pi/6]},   {-1, 
0} , {-Cos[Pi/6], -Sin[Pi/6]},    {-Cos[(2 Pi)/6], -Sin[(2 Pi)/
  6]}, {0, -1},   {Cos[(2 Pi)/6], -Sin[(2 Pi)/6]}, {Cos[
 Pi/6], -Sin[Pi/6]}, {1, 0}} ;

Graphics[{Thin, 
Line[ { L   }, 
VertexColors -> {Yellow, Red, Blue, Orange, Green, Red, Blue, 
 Orange, Green, Red, Blue}]}]

Now I am trying to merge the two. I noticed whenever I start of with the line command I can't get it to work with manipulate.

Manipulate[Thin, 
Line[ Plot[{{1, 0}, {2, 0}}, {x, 0, 3}], {a, 0, 2 Pi}  ]

So now I am not sure how to go about the problem since I can't even begin on it. Should I just use the equation of a line? That doesn't seem probably given the question

If you take a fraction f of a final vertex and a fraction 1-f of the corresponding initial vertex, and vary f between zero and one, you will find that a shape evolves from the initial shape to the final shape. Construct a Manipulate[] function with a slider that varies f that shows your straight line curling up into a circle.

Which makes me think that I need to have the individual vertices's in. Please help, thank you

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m = {#, 0} & /@ Range@13;
l = Table[{Cos[2 Pi n/12], Sin[2 Pi n /12]}, {n, 13}];
Manipulate[Graphics[{Thin, 
   Line[l, VertexColors -> {Yellow, Red, Blue, Orange, Green, Red, 
                            Blue, Orange, Green, Red, Blue}], 
   Line[m, VertexColors -> {Red, Blue, Orange, Green, Red, Blue, 
                            Orange, Green, Red, Blue, Orange, Green}],
   Line[f l + (1 - f) m]}], {f, 0, 1}]

Mathematica graphics

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  • $\begingroup$ @Megan Vineyard you can upvote an answer if you like it, too ;-) $\endgroup$ – Yves Klett Oct 22 '13 at 6:24

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