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### Rational viewing points in a polygon

We refer to the question posed in Seeing the vertices of a polygon with rational angles, but now ask for constructions or for the existence of rational viewing points. We'll call a point $p$ inside ...

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### Looking for product of symmetric polynomials evaluated at roots of unity

Consider $a_{1} = \alpha^{N-n}, a_{2} = \alpha^{N-n+1}, a_{3} = \alpha^{N-n+2}, a_{4} = \alpha^{N-n+3}, \cdots, a_{n} = \alpha^{N-1}$ where $\alpha$ is a complex $N$th root of unity where $N = 2 + ...