Polar equation for a Heptagon

Question

What is polar equation of a Heptagon ? I need to move some Android views in the form of a heptagon, for I need to have polar equations for Heptagon like for $x= r\sin(\theta)$ and $y=r\cos(\theta)$.

Is it possible to have polar equation for a heptagon too ?

Its 6 sided, it would be great i could get it for 7 or 8 sided polygon ! — Charan Pai, May 06 '14 at 10:04
^ but not at that (accepted) answer, but rather the one below it, which gives a polar equation for general $n$. — , Dec 31 '14 at 06:40

score 1 · Answer 1 · answered May 06 '14 at 10:12

1

A general formula for a regular polygon of radius $r$ with $n$ sides, denote $c_n = \cos(\pi/n)$, $s_n = \sin(\pi/n)$ and

$$f_n(x+iy) = \left||rs_n - |y|| - (rs_n - |y|)\right| + |x-rc_n|$$

then your polygon is given by

$$\prod_{k = 0}^{n-1} f_n\left(e^{-\frac{2 i k \pi}{n}} (x+iy)\right) = 0$$

(For heptagone $n = 7$).

answered May 06 '14 at 10:12

SweetWisher ツ

111

I need polar equations :( in terms of Theta – Charan Pai May 06 '14 at 11:20

Polar equation for a Heptagon

1 Answers1