Yitao Luo

Reinhardt's Maximum-Perimeter Polygon Problem for n=16, 32, and 64

A convex polygon is called small if its diameter is at most one. Reinhardt proved the universal perimeter bound $\operatorname{perim}(P)\le U_n:=2n\sin(\pi/(2n))$, and the bound is attained whenever $n$ has a nontrivial odd divisor. The remaining power-of-two cases have resisted exact solution beyond $n=8$. We give com...