3 problems

Let $P$ be a harmonic polygon with area $A$, sidelengths $s_i$, and angles $\theta_i$ as used in the paper. Sine-angle invariant conjecture. The quantity … is invariant. Equivalent…

Let $\mathcal{H}$ be a Poncelet family of $N$-gons interscribed between two homothetic, concentric ellipses, and let $A_1$ and $A_2$ be the areas of the two lateral harmonic polygo…

Let $P$ be a harmonic $N$-gon, let $Q$ be a point, and let $P'$ be the $N$-gon obtained by inverting the vertices of $P$ in a circle centered at $Q$. Let $\mathcal{S}$ be the Schou…