ngon[p_, q_] :=Polygon[Table[{Cos[2 Pi k q/p], Sin[2 Pi k q/p]}, {k, p}]];
F[{x_, y_}] := {y, x*y}; r[t_] := {Cos[t], Sin[t]}; l[w_] := Sqrt[w.w];
Manipulate[
VectorPlot[F[{x,y}], {x, -1, 1}, {y, -1, 1}];
NSum[F[r[t]].(r[t] + 2 Pi/n - r[t]), {t, 0, 2 Pi-2 Pi/n,2 Pi/n}];
Graphics[{Circle[],{EdgeForm[Red], Transparent, ngon[n, l]}}],{n,1,20,1},{l, 1, 20,1}]