First Advisor
J.J.P. Veerman
Date of Award
Winter 3-22-2024
Document Type
Thesis
Degree Name
Bachelor of Science (B.S.) in Mathematics and University Honors
Department
Mathematics and Statistics
Language
English
Subjects
Number theory, Ergodic theory
DOI
10.15760/honors.1463
Abstract
This thesis presents a surprising result that the difference in certain sums of constant rotations by the golden mean approaches exactly 1/5. Specifically, we focus on the Birkhoff sums of these rotations, with the number of terms equal to squared Fibonacci numbers. The proof relies on the properties of continued fraction approximants, Vajda's identity and the explicit formula for the Fibonacci numbers.
Rights
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Persistent Identifier
https://archives.pdx.edu/ds/psu/41386
Recommended Citation
Moore, Heather, "Birkhoff Summation of Irrational Rotations: A Surprising Result for the Golden Mean" (2024). University Honors Theses. Paper 1432.
https://doi.org/10.15760/honors.1463