Fibonacci Numbers

Mentor/s

Hema Gopalakrishnan

Paper Talk

Abstract

The Fibonacci sequence is defined as the sequence Fn with the recurrence relation Fn+1 = Fn + F n-1 where F0 = 0 and F1= 1. A closely related sequence to the Fibonacci sequence is the Lucas sequence, Ln. The terms of the Lucas sequence satisfy the the same recurrence relation as the Fibonacci sequence with differing initial conditions. In this paper, we will study some of the properties of the Fibonacci numbers and explore some of the relationships between Fibonacci and Lucas numbers. We will also give a proof of Binet's explicit formula for computing the nth Fibonacci number.

Mathematics

Location

Session 5: Digital Commons & Martire Room 217

Start Day/Time

4-25-2024 12:30 PM

End Day/Time

4-25-2024 1:45 PM

Students' Information

Maya Salamone, Mathematics Major, 2024 Graduation

Prize Categories

Most Scholarly Impact or Potential, Most Creative, Best Writing

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Apr 25th, 12:30 PM Apr 25th, 1:45 PM

Fibonacci Numbers

Session 5: Digital Commons & Martire Room 217

The Fibonacci sequence is defined as the sequence Fn with the recurrence relation Fn+1 = Fn + F n-1 where F0 = 0 and F1= 1. A closely related sequence to the Fibonacci sequence is the Lucas sequence, Ln. The terms of the Lucas sequence satisfy the the same recurrence relation as the Fibonacci sequence with differing initial conditions. In this paper, we will study some of the properties of the Fibonacci numbers and explore some of the relationships between Fibonacci and Lucas numbers. We will also give a proof of Binet's explicit formula for computing the nth Fibonacci number.