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Uniformity of cube lines and related problems

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TitleInfo
Title
Uniformity of cube lines and related problems
Name (type = personal)
NamePart (type = family)
Donders
NamePart (type = given)
Michael
NamePart (type = date)
1990-
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Michael Donders
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author
Name (type = personal)
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Beck
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Jozsef
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Jozsef Beck
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Advisory Committee
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chair
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Kopparty
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Swastik
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Swastik Kopparty
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Advisory Committee
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internal member
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Kontorovich
NamePart (type = given)
Alex
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Alex Kontorovich
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Advisory Committee
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internal member
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Bumby
NamePart (type = given)
Richard
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Richard Bumby
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Advisory Committee
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outside member
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Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
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school
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2017
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2017-05
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2017
Place
PlaceTerm (type = code)
xx
Language
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eng
Abstract (type = abstract)
We define a cube line to be a geodesic traveling over the surface of the cube; that is---we take a straight line traveling on one of the faces of a cube, and when it hits an edge it continues on to the next face so that if the two faces were unfolded to be coplanar, the two line segments on either face would connect to form a straight line. The principal question we look to answer is: does this cube line uniformly distribute over the surface of the cube. Here, we define uniformly distributed as, for any Jordan measurable test set, the proportion of the cube line which lies in the test set approaches the relative size of the test set as the length of the cube line approaches infinity. This problem was derived as an extension to the classical problems of uniform distribution of a torus line over a unit square and uniform distribution of billiard paths over a unit square. The arguments in this problem, however, are quite different from these previous problems, and take ideas from many fields, including erogidc theory, number theory, geometry and combinatorics.
Subject (authority = RUETD)
Topic
Mathematics
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Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
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ETD_7936
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (iv, 124 p. : il..)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Michael Donders
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T38055FC
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Donders
GivenName
Michael
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2017-04-05 03:18:06
AssociatedEntity
Name
Michael Donders
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Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
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Name
Author Agreement License
Detail
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
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

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2017-07-31T09:26:29
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