2 problems

Let a small $n$-gon be a convex polygon in the plane with $n\geq 3$ vertices and diameter at most one. An optimal small $n$-gon is one attaining the maximum possible perimeter amon…

Let a small $n$-gon be a convex polygon in the plane with $n\geq 3$ vertices and diameter at most one. A diameter chord is a side or diagonal of length one. For even $n$, the conje…