Helly-Type Theorems on Support Lines for Families of Congruent Disks in the Plane

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dc.contributor.advisorSoltan, Valeriu
dc.contributor.authorRuss, Tyler R.
dc.date.accessioned2024-03-29T21:12:23Z
dc.date.available2024-03-29T21:12:23Z
dc.date.issued2023-12
dc.description.abstractIn this dissertation, we consider the problem to determine Helly-type numbers for support lines of nonoverlapping families of congruent disks in the plane. This problem, originally posed by R. Dawson for the case of disjoint families of convex bodies and by V. Soltan for the case of disjoint families of unit disks, has been recently solved. This research generalizes to the case of non-overlapping families of congruent disks. An essential part of the argument is based on the study of "critical" families of congruent disks.
dc.format.mediumdoctoral dissertations
dc.identifier.orcid0000-0001-7657-093X
dc.identifier.urihttp://hdl.handle.net/1920/13559
dc.identifier.urihttps://doi.org/10.13021/MARS/2035
dc.language.isoen
dc.rightsCopyright 2023 Tyler R. Russ
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0
dc.subjectcombinatorial
dc.subjectdisks
dc.subjectgeometry
dc.subjectHelly
dc.subjectplane
dc.subjectsupport line
dc.titleHelly-Type Theorems on Support Lines for Families of Congruent Disks in the Plane
dc.typeDissertation
thesis.degree.disciplineMathematics
thesis.degree.grantorGeorge Mason University
thesis.degree.levelDoctoral
thesis.degree.namePhD in Mathematics

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