  We use Batson's lower bound on the nonorientable slice genus of
$(2n,2n-1)$-torus knots to prove that for any $n \geq 2$, every smooth Jordan
curve has an inscribed rectangle of of aspect ratio $\tan(\frac{\pi k}{2n})$
for some $k\in \{1,...,n-1\}$. Setting $n = 3$, we have that every smooth
Jordan curve has an inscribed rectangle of aspect ratio $\sqrt{3}$.
