Talk:Equation of regular polygon/@comment-50.45.146.186-20140706180100

But, can you do it *without* Floor or Mod?

I can do it for EVEN polygons using a Sigma series, but ODDS are yet elusive:

v = 14 (* v=number of vertices of the polygon. v must be an even integer >= 4. *) n = v/2 (* n = number of terms in numerator/denimonator Sigma \ series(es). *) PolarPlot[(Sum[Abs[Cos[((n + 2 + 2 (k - 1)) Pi)/(2 n)]], {k, 1, n}])/(Sum[Abs[Cos[x + (((n + 2 + 2 (k - 1)) Pi)/(2 n))]], {k, 1, n}]), {x, 0, 2 Pi}]

The above is Mathematica code for plotting an even-sided polygon with sides / vertices >= 4 in Polar Form.

Would be interesting to know if anyone can do the same for ODD-sided polygons! ^_^ No Mod[] or Floor[] allowed, only continuous Sin[] / Cos[] functions!

~Michael Gmirkin