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    The Isoperimetric Inequality on Natural Subsets

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    Date
    2017-05-24
    Author
    Jansma, Harrison
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    Abstract
    The isoperimetric problem is an exercise of classical geometry posing the following question. If a closed Jordan region on the plane has area A, what is the smallest perimeter that the gure can attain? This question was solved, yet recently an interesting reformulation of the question was posed. By viewing sets of natural numbers as objects, volume was defined as the sum of a sets elements, while perimeter was defined as the sum of all elements in a set with adjacent numbers not contained in a set. This new isoperimetric problem over the naturals then posed the question, If a subset of 0,1,2,... has volume n, what is the smallest possible value of its perimeter. In this thesis we seek to create tight bounds on this perimeter function, as well as construct an explicit set of minimal perimeter for all natural numbers.
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    http://hdl.handle.net/2104/10007
    Department
    Baylor Business Fellows.
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    • Theses - Honors College

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    Copyright © Baylor® University All rights reserved. Legal Disclosures.
    Baylor University Waco, Texas 76798 1-800-BAYLOR-U
    Baylor University Libraries | One Bear Place #97148 | Waco, TX 76798-7148 | 254.710.2112 | Contact: libraryquestions@baylor.edu
    If you find any errors in content, please contact librarywebmaster@baylor.edu
    DSpace software copyright © 2002-2016  DuraSpace
    Contact Us | Send Feedback
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    Theme by 
    Atmire NV