Suppose that \( \Pi \) is a closed polygon in the plane. If \( \Pi \) is equilateral \( k \)-gon, and if \( A \) is the area of \( \Pi \), and \( L \) the length of its boundary, prove that
\[
\frac{A}{L^2} \leq \frac{1}{4k} \cot \frac{\pi}{k} \leq \frac{1}{4\pi}.
\]

The best solution was submitted by 윤창기 (서울대학교 화학과). Congratulations!

Here is his solution of problem 2019-01.

Similar solutions were submitted by 길현준 (2018학번, +3), 조재형 (수리과학과 2016학번, +3), 김태균 (수리과학과 2016학번, +2). Alternative solution was submitted by 고성훈 (2018학번, +3). Four incorrect solutions were received.