Title

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.

Location

ECL 114

Start Date

3-25-2023 10:00 AM

Presentation Format

Oral Only

Group Project

Yes

COinS
 
Mar 25th, 10:00 AM

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.