The biggest little polygon

Formal definition

• ContainerUnconstrained in the plane: the only global constraint is diameter at most 1, with coordinates written inside [0, 1.5] × [0, 1.5]
• SubmissionExactly n points
• ConstraintsAll pairwise distances are at most 1, and every point is a strict vertex of the convex hull
• Areaqᵢ = (xᵢ,yᵢ) are the hull vertices ordered counterclockwise by the verifier (submissions need not be pre-sorted); internally, the verifier compares the shoelace value 2A(P) in exact arithmetic$$A\left(P\right)=\frac{1}{2}\left|\sum _{i=1}^n\left(x_i{y}_{i+1}-x_{i+1}{y}_i\right)\right|,q_{n+1}=q_1$$
• ObjectiveMaximize the area A(P) over all convex n-gons P of diameter at most 1$$\underset{P}{\max }A\left(P\right)$$