  We show that for the regular n-simplex, the 1-codimensional central slice
that's parallel to a facet will achieve the minimum area (up to a 1-o(1)
factor) among all 1-codimensional central slices, thus improving the previous
best known lower bound (Brzezinski 2013) by a factor of $\frac{2\sqrt{3}}{e}
\approx 1.27$. In addition to the standard technique of interpreting geometric
problems as problems about probability distributions and standard
Fourier-analytic techniques, we rely on a new idea, mainly \emph{changing the
contour of integration} of a meromorphic function.
