In a recent publication, Jack E. Graver describes a method for computing terms in the Calkin-Wilf sequence. First, we explore an original method which uses continued fractions to evaluate and locate terms in the Calkin-Wilf sequence. Then, we extend the Calkin-Wilf tree to include all of the rational numbers exactly once each. Another generalization of the tree characterizes the relationship between rational numbers and continued fractions with integer coefficients. From a shift in perspective, we study infinite continued fractions and irrational numbers, and their relationships with Calkin-Wilf paths. The highly regarded result in this section is an original explanation for why irrational square roots of positive rational numbers have periodic continued fractions with palindromic coefficients. Finally, we exhibit a matrix analogue of the Calkin-Wilf tree and use its properties to conclude which irrational numbers have periodic continued fractions.

Creator

• Gobler, Benjamin

Colaboradores

• Servatius, Herman
• Servatius, Brigitte

Degree

• MS

Unit

• Mathematical Sciences

Publisher

• Worcester Polytechnic Institute

Identifier

• etd-107136

Palavra-chave

• continued fractions
• Euclidean algorithm
• Calkin-Wilf

Advisor

• Servatius, Herman
• Servatius, Brigitte

Defense date

• 2023-04-27

Year

• 2023

Date created

• 2023-04-30

Resource type

• Thesis

Source

• etd-107136

Rights statement

• In Copyright

Última modificação

• 2023-06-01