Bachelor of Arts (BA)
Department or Program
Michael M. Kash
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.
Juillerat, Jacob A., "Transcendental Numbers" (2016). Senior Theses.