4 problems

Let $\alpha_n$ be the generalized Heron polynomial associated with an $n$-gon, and let … Here $\mathrm{S}$ denotes the signed area of the polygon. Robbins' monicity conjecture. Bas…

Let a cyclic polygon have area $A$. Consider the polynomial equation in $(4A)^2$ whose coefficients are polynomials in the elementary symmetric functions of the squared side length…

Let a uniform cyclic quadrilateral have angles ${\Greekmath 010B}$, ${\Greekmath 010C}$, and ${\Greekmath 0121}$. The cyclic quadrilateral joint-density conjecture. The joint densi…

Let a uniform cyclic $6$-gon have consecutive polygonal angles $reekmath 010B]$, $reekmath 010C]$, $reekmath 010D]$, $reekmath 010E]$, and let ${\Greekmath 0119}$ denote the releva…