# Polar equation for a Heptagon [duplicate]

This question already has an answer here:

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 ?

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## marked as duplicate by sandwich, Mike Miller, Claude Leibovici, Avitus, Swapnil TripathiDec 31 '14 at 9:22

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

You solution lies here – SweetWisher ツ May 6 '14 at 10:02
Its 6 sided, it would be great i could get it for 7 or 8 sided polygon ! – Charan Pai May 6 '14 at 10:04
then have a look here – SweetWisher ツ May 6 '14 at 10:06
^ but not at that (accepted) answer, but rather the one below it, which gives a polar equation for general $n$. – sandwich Dec 31 '14 at 6:40

## 1 Answer

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 $n = 7$).

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I need polar equations :( in terms of Theta – Charan Pai May 6 '14 at 11:20