Class Year

2016

Date

4-25-2016

Document Type

Thesis

Distinguished Thesis

Yes

Degree Name

Bachelor of Arts (BA)

Department or Program

Mathematics

First Advisor

Enrique Treviño

Second Advisor

DeJuran Richardson

Third Advisor

Michael M. Kash

Abstract

The numbers e and π are transcendental numbers, meaning each of them are not the root of any polynomial with rational coefficients. We prove that e and π are transcendental numbers. The original proofs use the Fundamental Theorem of Symmetric Polynomials and Stirling’s Formula, which we develop and prove. Since π is not algebraic, neither is √π, which answers the ancient question of whether one can square a circle. The proof that π is transcendental is a beautiful example of how higher level mathematics can be used to answer ancient questions.


Included in

Mathematics Commons

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