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

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.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Mathematics & Statistics

Grantor dc:publisher.institution

Science

Year dc:date.issued

2023

Author dc:creator

• Strachan, Cameron

Advisor dc:contributor.advisor

• Bezdek, Karoly

Committee members dc:contributor.committeemember

• Bezdek, Karoly
• Hamilton, Ryan
• Zinchenko, Yuriy

• Euclidean Geometry
• Illumination
• Cap Body
• Spiky Ball
• Convex Geometry
• C-polygons

Statement 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.

Language dc:language.iso

en

DOI

https://dx.doi.org/10.11575/PRISM/41539

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:1880/116697