The Illumination of Symmetric Spiky Balls and Cap Bodies; and a note on the Vertex Classification of Planar C-polygons

Strachan, Cameron

The Illumination of Symmetric Spiky Balls and Cap Bodies; and a note on the Vertex Classification of Planar C-polygons

dc.contributor.advisor	Bezdek, Karoly
dc.contributor.author	Strachan, Cameron
dc.contributor.committeemember	Bezdek, Karoly
dc.contributor.committeemember	Hamilton, Ryan
dc.contributor.committeemember	Zinchenko, Yuriy
dc.date	2023-11
dc.date.accessioned	2023-07-06T16:36:34Z
dc.date.available	2023-07-06T16:36:34Z
dc.date.issued	2023-06
dc.description.abstract	This thesis handles two problems in the field of convex geometry. The first, is the problem of illuminating the boundary of Euclidean shapes known as spiky balls and cap bodies in various dimensions. Specifically we consider illuminating the cases where a spiky ball is 2-illuminable, and the cases where a cap body is symmetric, either centrally or unconditionally. The second problem we investigate is how complex the boundary structure of a C-polygon can be, which is a finite intersection of homothets of a particular convex domain C; and how this boundary structure depends on C.
dc.identifier.citation	Strachan, C. (2023). The illumination of symmetric spiky balls and cap bodies; and a note on the vertex classification of planar C-polygons (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.uri	https://hdl.handle.net/1880/116697
dc.identifier.uri	https://dx.doi.org/10.11575/PRISM/41539
dc.language.iso	en
dc.publisher.faculty	Science
dc.publisher.institution	University of Calgary
dc.rights	University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subject	Euclidean Geometry
dc.subject	Illumination
dc.subject	Cap Body
dc.subject	Spiky Ball
dc.subject	Convex Geometry
dc.subject	C-polygons
dc.subject.classification	Mathematics
dc.title	The Illumination of Symmetric Spiky Balls and Cap Bodies; and a note on the Vertex Classification of Planar C-polygons
dc.type	master thesis
thesis.degree.discipline	Mathematics & Statistics
thesis.degree.grantor	University of Calgary
thesis.degree.name	Master of Science (MSc)
ucalgary.thesis.accesssetbystudent	I do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.