Mentor/s
Hema Gopalakrishnan
Participation Type
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.
College and Major available
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
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Prize Categories
Most Scholarly Impact or Potential, Most Creative, Best Writing
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.
Students' Information
Maya Salamone, Mathematics Major, 2024 Graduation