Proof of a New Fibonacci Identity
School Name
James Island Charter High School
Grade Level
10th Grade
Presentation Topic
Mathematics
Presentation Type
Mentored
Abstract
A second order recurrence relation Fn is called Fibonacci sequence if it satisfies that F0=0, F1=1, and Fn= Fn-1+Fn-2 for n ≥3. Fibonacci used this sequence to model the breeding of a population of rabbits. Fibonacci numbers are also connected to many other different topics of pure mathematics, applied mathematics, art, and economy including number theory, binomial coefficients, Pascal's triangle, Wall Street stock market, and the Milky Way. In this presentation we show the solution of a new identity related to Fibonacci numbers. This was an open problem that appeared in The Fibonacci Quarterly as B-1305. Our original solution was submitted for publication to the same journal and is under consideration.
Recommended Citation
Rhett Smith, Virginia and Torek, Ell, "Proof of a New Fibonacci Identity" (2023). South Carolina Junior Academy of Science. 94.
https://scholarexchange.furman.edu/scjas/2023/all/94
Location
ECL 114
Start Date
3-25-2023 10:00 AM
Presentation Format
Oral Only
Group Project
Yes
Proof of a New Fibonacci Identity
ECL 114
A second order recurrence relation Fn is called Fibonacci sequence if it satisfies that F0=0, F1=1, and Fn= Fn-1+Fn-2 for n ≥3. Fibonacci used this sequence to model the breeding of a population of rabbits. Fibonacci numbers are also connected to many other different topics of pure mathematics, applied mathematics, art, and economy including number theory, binomial coefficients, Pascal's triangle, Wall Street stock market, and the Milky Way. In this presentation we show the solution of a new identity related to Fibonacci numbers. This was an open problem that appeared in The Fibonacci Quarterly as B-1305. Our original solution was submitted for publication to the same journal and is under consideration.
