The dynamical system of iterated Cevian Tribbles

Thumbnail Image
Date
2016-01-01
Authors
Carroll, Emily
Major Professor
Advisor
Arka P. Ghosh
Alexander Roitershtein
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Organizational Unit
Journal Issue
Is Version Of
Versions
Series
Department
Mathematics
Abstract

Ceva's Theorem gives a necessary and sufficient condition for three lines through the vertices of a triangle to intersect at a single point. We investigate what happens when that condition is not met, which means the three lines form a triangle inside the original (called a Tribble), and the process is iterated. By Cantor's Intersection Theorem, we know that the Tribbles will converge to a point within the initial triangle as long as the side lengths of the Tribbles go to zero. We consider different ways to iterate this process. We establish an nth term test for convergence when the Cevian ratios are deterministic sequences. We prove that when the Cevian ratios used to iterate are chosen at random, the Tribbles always converge. We initiate study on the distribution of limit points. With the aid of a simulation in MATLAB that produces graphical plots for the numerical estimations of Tribble limit points, we begin to visualize and describe the distribution of limit points.

Comments
Description
Keywords
Citation
Source
Subject Categories
Copyright
Fri Jan 01 00:00:00 UTC 2016