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arXiv · 2101.04037

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

Bikash Chakraborty·Sagar Chakraborty·Reza Farhadian
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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 $e<b$.

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Bikash Chakraborty, Sagar Chakraborty, Reza Farhadian. 2021-01-11. Geometric visualizations of $b^{e}<e^{b}$ when $e<b$. https://arxiv.org/abs/2101.04037

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