2022 Summer Undergraduate Research Program (SURP) Symposium

Location

ScholarSpace, Rod Library, University of Northern Iowa

Presentation Type

Open Access Poster Presentation

Document Type

poster

Keywords

Metric spaces;

Abstract

The concept of a rendezvous number was originally developed by O. Gross in 1964, and was expanded upon greatly by J. Cleary, S. Morris, and D. Yost in 1986. This number exists for every metric space, yet very little is known about it, and it’s exact value for most spaces is not known. Furthermore, it’s exact value is difficult to calculate, and in most cases we can only find bounds for the value. We focused on their arguments using convexity and applied it to shapes in different metrics and graphs. Using sets of points that stood out (vertices, midpoints) as well as computer analysis, we attempted to find rendezvous numbers for certain geometric shapes and classes of graphs, all of which had been previously unknown.

Start Date

29-7-2022 11:00 AM

End Date

29-7-2022 1:30 PM

Event Host

Summer Undergraduate Research Program, University of Northern Iowa

Faculty Advisor

Bill Wood

Department

Department of Mathematics

File Format

application/pdf

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Jul 29th, 11:00 AM Jul 29th, 1:30 PM

Rendezvous Numbers of Compact and Connected Spaces

ScholarSpace, Rod Library, University of Northern Iowa

The concept of a rendezvous number was originally developed by O. Gross in 1964, and was expanded upon greatly by J. Cleary, S. Morris, and D. Yost in 1986. This number exists for every metric space, yet very little is known about it, and it’s exact value for most spaces is not known. Furthermore, it’s exact value is difficult to calculate, and in most cases we can only find bounds for the value. We focused on their arguments using convexity and applied it to shapes in different metrics and graphs. Using sets of points that stood out (vertices, midpoints) as well as computer analysis, we attempted to find rendezvous numbers for certain geometric shapes and classes of graphs, all of which had been previously unknown.