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Proof without Words: \(\pi^e < e^{\pi}\)

by Fouad Nakhli

This article originally appeared in:
Mathematics Magazine
June, 1987

Subject classification(s): Inequalities | Comparison of numbers | Famous Numbers
Applicable Course(s): 4.1 Introduction to Proofs | 4.3 Number Theory

The author presents a geometric proof of \(\pi^e < e^{\pi}\) by using a suitable function.

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Capsule Course Topic(s):
Number Theory | Numbers With Special Forms or Properties
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