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The isoperimetric problem
Descriptive
TitleInfo
Title
The isoperimetric problem
Name
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Forte
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Paul
NamePart
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1983-
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Paul Forte
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author
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Fu
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Siqi
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Siqi Fu
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Advisory Committee
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chair
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Rutgers University
Role
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degree grantor
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Camden Graduate School
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school
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theses
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2020
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2020-05
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English
Abstract
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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.
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.
Subject
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Topic
Isoperimetric inequalities
Subject
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Topic
Mathematics
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Rutgers University Electronic Theses and Dissertations
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ETD_10984
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1 online resource (v, 42 pages) : illustrations
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M.S.T.
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Includes bibliographical references
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Camden Graduate School Electronic Theses and Dissertations
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rucore10005600001
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doi:10.7282/t3-vpb2-5s64
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ETD graduate
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Rights
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The author owns the copyright to this work.
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Name
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Forte
GivenName
Paul
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Permission or license
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2020-05-26 10:56:03
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Paul Forte
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Rutgers University. Camden Graduate School
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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Microsoft: Print To PDF
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