Aleyna Bulduk: Talet e och dess historia

Abstract.

The number \(e\), otherwise known as Euler’s number, is one of the most famous numbers in mathematics. Students encounter this number usually in the context of exponential functions and logarithms, in which they acquire that the number is the base of the natural logarithm ln. Besides that, rarely any facts regarding its origin and properties are given, which, in general, creates gaps in knowledge among students. Against this background, this paper aims to contribute to a deeper understanding of the number \(e\). In this study, we will thus explore the history of the number, prove that it is an irrational and even a transcendental number, derive its continued fraction expansion, as well as discuss and compare some of the number’s approximation methods, including limit, series, and continued fraction.