Author

Dawid Trela

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Preprint Aug 2026

Maximum-Area Small Polygons of Even Order

A small n-gon is a planar n-gon whose diameter is at most one. For odd n, Reinhardt proved that the regular polygon is optimal. For even n, the maximizer is nonregular, and only a few low orders were known exactly. We prove that for every even n>= 8 the maximum-area small n-gon is unique up to Euclidean isometry and re...

Dawid Trela · 1 citation · ⚡1

Preprint Aug 2026

Boundary Layers and Sharp Asymptotics for Maximum-Area Small Polygons

A small polygon is a planar polygon of diameter at most one; let $A_n$ be the largest area at order $n$. Using the global characterization of the even-order maximizers established in a companion paper, we determine their asymptotic geometry. After scaling the angular deficits near the unique pendant diameter, the exact...

Dawid Trela · 0 citations