Home
Resource
Uniformity of cube lines and related problems
PDF
PDF format is widely accepted and good for printing.
Plug-in required
PDF-1(561.27 kb)
Citation & Export
View Usage Statistics
Staff View

Citation & Export
Hide

Simple citation

Donders, Michael. Uniformity of cube lines and related problems. Retrieved from https://doi.org/doi:10.7282/T38055FC

Export

Click here for information about Citation Management Tools at Rutgers.

Statistics
Hide

Description

TitleUniformity of cube lines and related problems
NameDonders, Michael (author); Beck, Jozsef (chair); Kopparty, Swastik (internal member); Kontorovich, Alex (internal member); Bumby, Richard (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2017
Other Date2017-05 (degree)
SubjectMathematics
Extent1 online resource (iv, 124 p. : il..)
DescriptionWe 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.
NotePh.D.
NoteIncludes bibliographical references
Noteby Michael Donders
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T38055FC
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
Version 8.5.5
Rutgers University Libraries - Copyright ©2024