On Surprising Approximations Involving Multiple Mathematical Constants

Abstract

In this article, we present new numerical approximations involving five numerical constants, namely the Pi constant, the Euler constant, the Euler-Mascheroni constant, the Catalan constant, and the golden ratio constant. Four of these constants can be simply approximated by the others with relative accuracy. These results have potential applications in mathematics education by providing an accessible framework for exploring the connections between fundamental constants. In a sense, they also promote a deeper conceptual understanding of numerical analysis.