AlphaEvolve problems·alphaevolve:9

Kakeya needle problem

Let $n \\geq 2$. Let $C^T(n)$ denote the minimal area $|\\bigcup_{j=1}^n T_j|$ of a union of triangles $T_j$ with vertices $(x_j,0)$, $(x_j + 1/n, 0)$, $(x_j + j/n, 1)$ for some real numbers $x_1,\\dots,x_n$, and similarly define $C^P(n)$ denote the minimal area $|\\bigcup_{j=1}^n P_j|$ of a union of parallelograms $P_j$ with vertices $(x_j,0), (x_j+1/n,0), (x_j+j/n,1), (x_j+(j+1)/n,0)$ for some r

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