Euler's Number : A closer look at an approximation of e using Leonard Euler's Theory of Continued Fractions
Presenter(s)
Libby Kreikemeier
Files
Description
Leonard Euler created a Theory of Continued Fractions for approximating any number in the set of Real numbers. With the use of the division algorithm we are able to simplify a fraction into a set of convergents further allowing us to approximate the fraction into a decimal. This theory can be applied to many numbers of different forms like 3, 235/19, and pi. Euler’s number, e, is approximately equivalent to 2.718, and is used as a constant in many areas of mathematics and science. It is most commonly used in exponential growth and decay, compound interest, and differential equations. With these many applications, it is important to have a general understanding of what this constant is despite its irrationality and non-terminating decimal points. Because e is an irrational real number, the Theory of Continued Fractions can be applied, allowing us to easily approximate e.
Publication Date
4-23-2025
Project Designation
Capstone Project
Primary Advisor
Rebecca J. Krakowski
Primary Advisor's Department
Mathematics
Keywords
Stander Symposium, College of Arts and Sciences
Institutional Learning Goals
Scholarship; Vocation
Recommended Citation
"Euler's Number : A closer look at an approximation of e using Leonard Euler's Theory of Continued Fractions" (2025). Stander Symposium Projects. 4134.
https://ecommons.udayton.edu/stander_posters/4134
Comments
1:15-2:30, Kennedy Union Ballroom