Exploring Diagonals in the Calkin-Wilf Tree

Author Information

Matthew Gagne

Abstract/Description

For centuries, people have been interested in patterns. Even in that which appears random, humans have been trying to understand the underlying order of things. Mathematicians throughout time have studied many phenomena, including infinite sequences of numbers and have been able, at times, to see structure. Many have found the satisfaction, even joy, of discovering patterns in sequences. A typical way to describe this is by a recursive formula. A recursive definition defines a term in the sequence using the previous terms in the sequence. Even more satisfying than a recursive formula is a closed formula. With this, one can find the number at any position in the sequence. A closed formula is like a locksmith cutting a master key for every lock in a building.

Note on the Author

Matthew Gagne graduated from Bridgewater with a degree in Mathematics in January 2013. His research, made possible by an Adrian Tinsley Summer Research Grant, was mentored by Dr. Shannon Lockard of the BSU mathematics department.

Recommended Citation

Gagne, Matthew (2013). Exploring Diagonals in the Calkin-Wilf Tree. Undergraduate Review, 9, 37-40.
Available at: https://vc.bridgew.edu/undergrad_rev/vol9/iss1/11

Rights Statement

Articles published in The Undergraduate Review are the property of the individual contributors and may not be reprinted, reformatted, repurposed or duplicated, without the contributor’s consent.