The Isoperimetric Inequality on Natural Subsets

dc.contributor.advisorSimanek, Brian
dc.contributor.authorJansma, Harrison
dc.contributor.departmentBaylor Business Fellows.en_US
dc.contributor.otherBaylor University.en_US
dc.contributor.schoolsHonors College.en_US
dc.date.accessioned2017-05-24T23:53:29Z
dc.date.available2017-05-24T23:53:29Z
dc.date.copyright2017
dc.date.issued2017-05-24
dc.description.abstractThe 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.en_US
dc.identifier.urihttp://hdl.handle.net/2104/10007
dc.language.isoen_USen_US
dc.rightsBaylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.en_US
dc.rights.accessrightsWorldwide accessen_US
dc.subjectMathematicsen_US
dc.subjectNumber Theoryen_US
dc.subjectPartitionsen_US
dc.titleThe Isoperimetric Inequality on Natural Subsetsen_US
dc.typeThesisen_US

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