Research Publication Title

Various Properties of the Fibonacci Number Sequence

Major

Mathematics

Faculty Mentor(s)

Brandon L. Samples

Abstract

The Fibonacci number sequence is famous for its connection to the Golden Ratio and its appearance within natural objects. However, there do exist Fibonacci-like sequences that share the same recursive definition as the Fibonacci sequence without possessing its same connection to the Golden Ratio. We will first explain a method for constructing such Fibonacci-like sequences using the relationship between the closed formula for the Fibonacci sequence and its corresponding matrix. We will then examine the relationship between the Golden Ratio and the Fibonacci number sequence through the appearance of Fibonacci numbers within the curves inside the head of a sunflower.

Start Date

10-4-2015 12:15 PM

End Date

10-4-2015 1:00 PM

Location

HSB 3rd Floor Student Commons

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Apr 10th, 12:15 PM Apr 10th, 1:00 PM

Various Properties of the Fibonacci Number Sequence

HSB 3rd Floor Student Commons

The Fibonacci number sequence is famous for its connection to the Golden Ratio and its appearance within natural objects. However, there do exist Fibonacci-like sequences that share the same recursive definition as the Fibonacci sequence without possessing its same connection to the Golden Ratio. We will first explain a method for constructing such Fibonacci-like sequences using the relationship between the closed formula for the Fibonacci sequence and its corresponding matrix. We will then examine the relationship between the Golden Ratio and the Fibonacci number sequence through the appearance of Fibonacci numbers within the curves inside the head of a sunflower.