Alex Eustis

Harvey Mudd College Mathematics 2005

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Thesis Proposal: Negative Continued Fractions
Thesis Advisor: Arthur T. Benjamin
Second Reader: Prof. Sanji Gupta (Scripps College)
E-Mail: aeustis@hmc.edu
Midyear Report: The Negs and Regs of Continued Fractions
Senior Thesis: The Negs and Regs of Continued Fractions
Presentation Days poster: The Negs and Regs of Continued Fractions

The Negs and Regs of Continued Fractions

There are two main aims of this thesis. The first is to further develop and demonstrate applications of the combinatorial interpretation of continued fractions introduced in professor Benjamin's book, Proofs That Count (MAA, 2003). The second is to investigate the theory of negative continued fractions, a relatively unresearched topic. That is, discuss the ways in which they are similar to and different from the regular class, describe how to convert between the two forms, and show that the central theorems concerning regular continued fractions also apply to the negative ones.