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, continued fraction approximant, Fibonacci sequence, Birkhoff sum, rotation

DOI

10.15760/honors.1463

Abstract

This thesis presents a surprising result that the difference in a 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

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

Persistent Identifier

https://archives.pdx.edu/ds/psu/41386

Share

COinS