Geometric visualizations of $b^e<e^b$ when $e<b$

Abstract

In connection to the two fascinating constants $e$ and $\pi$, there are many beautiful visual proofs to the inequality ${\pi }^e<e^{\pi }$. The aim of this classroom capsule is to give three visual proofs to the more general inequality $b^e<e^b$ where $e<b$.

3 pages, 3 figures