Which is greater: \boldsymbole^π or \boldsymbolπ^e? An unorthodox solution to a classic puzzle

2023/09/09 by Vallejo, Andrés, Bove, Italo
#Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences #History and Overview (math.HO)

paper · doi:10.48550/arxiv.2309.10826

Abstract

The question of the title is a famous puzzle in the field of recreational mathematics, and can be addressed by several approaches. A compilation of solutions, some of them very ingenious, can be found in [1]. In this contribution we present an alternative solution based on the second law of thermodynamics. The method can be extended to derive a more general result involving the exponential function.

Related

• Geometric visualizations of b^e
• Relations between e and π: Nilakantha's series and Stirling's formula
• Another look at e
• From e to π: Derivation of the Wallis formula for π from e
• Numbers in the base e^π