TY - JOUR
TI - The isoperimetric problem
DO - https://doi.org/doi:10.7282/t3-vpb2-5s64
PY - 2020
AB - The topic that I choose to study for this thesis was the isoperimetric problem which seeks to determine the plane figure of maximum area for a given perimeter. This is a problem in mathematics with a rich history. Although the solution, the circle, is already well known, proving the truth of this is rather difficult.
My main reference source in completing this thesis was the book Fourier Analysis by T. W. Körner. I also included information from other textbooks and academic papers. Where I found the author's explanations vague or insufficiently mathematically rigorous, I included my own original work.
The challenging aspect of this topic was proving the circle is the solution without first assuming that a solution exists. If one assumes that a solution to the isoperimetric problem must exist, then it can be arrived at with simple high school level geometric methods. However, as demonstrated in this thesis, the existence of a solution to the isoperimetric problem is not trivial.
The mathematically rigorous solutions that I included in this thesis utilized methods of calculus as well as Fourier analysis. The concepts that I incorporated from Fourier analysis; I had not studied prior to beginning my graduate coursework.
KW - Isoperimetric inequalities
KW - Mathematics
LA - English
ER -