O Número de Euler - Figueira, Ramon Formiga (2017)
The Euler's Number, denoted by e and corresponding to the base of the Natural Logarithms, despite being one of the most important constants in Mathematics, both by the variety of its mathematical implications and by the number of its practical applications, remains unknown to many people. It is common to nd Engineering or even Exact Sciences students who only became aware of the existence of e after taking a Calculus Course. It is also not di cult to nd students who, even after such contact, seem to never realize the importance of this number. The e is a versatile constant. Although, in general, it appears related to results involving Di erential and Integral Calculus, it is present in several problems of di erent Mathematics areas. We can nd it, besides Analysis and Function Theory, in Financial Mathematics, Combinatorial Analysis, Probability, Trigonometry, Geometry, Statistics, Number Theory. In this work, we make a brief historical analysis about the discovery of the Euler's Number, we present its de nition, as well as alternative ways of characterizing it through in nite sums and products. We also address two interesting problems in which it is present: the counting of the number of partitions of a nite non-empty set and obtaining an approximation for the factorial of a natural number, in which we nd the Stirling's Approximation.