Euler's Number : A closer look at an approximation of e using Leonard Euler's Theory of Continued Fractions

Euler's Number : A closer look at an approximation of e using Leonard Euler's Theory of Continued Fractions

    Presenter(s)

    Libby Kreikemeier

    Comments

    1:15-2:30, Kennedy Union Ballroom

    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

    Euler's Number : A closer look at an approximation of e using Leonard Euler's Theory of Continued Fractions

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