Real Life Applications of the Fibonacci Sequence in Natural and Economic Systems
Overview
This paper explores the practical applications of the Fibonacci sequence beyond its mathematical definition, examining its manifestation in natural systems such as tree branch growth and human anatomy, as well as in economic contexts like product pricing. The author presents empirical observations of tree measurements and theoretical examples to demonstrate that the Fibonacci sequence is a fundamental pattern governing sequential processes in both biological and commercial domains.
What this essay covers
- Introduction and definition of Fibonacci sequence with historical context of Leonardo Pisano
- Experimental study of tree branch growth patterns and measurements demonstrating Fibonacci application
- Real-world examples including human development, pricing mechanisms, and anatomical structures
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Real Life Fibonacci
Leonardo Pisano, nicknamed Fibonacci, discovered the Fibonacci numbers. The Fibonacci numbers are a sequence where each term is the summation of two numbers that precede it. It is a series of numbers where a number of results from the addition of two previous two numbers starting with zero and one. The sequence would appear as follows 0, 1, 1, 2, 3, 5, 8… As a rule, the sequence is written as Xn = Xn-1 + Xn-2 (Velasquez). Pisano used a case study of rabbits to develop this sequence. He aimed to determine how many tamed rabbits would be born, assuming that two rabbits gave birth every month to another two and began bearing young ones after two months. In a real-life Fibonacci experiment, I studied how trees grow and the sequence in which they develop branches. The outcome provides evidence of the Fibonacci sequence in real-life application.
I measured the distance between the ground distance to the branch of a tree. I also measured one branch to the next and the distance between the branch's junction from the main trunk to the next split within the branch. I repeated these measurements on three branches of the same tree. The distance from the ground to the first branch was 90 centimeters, while the distance from the first branch to the next was 45 centimeters. The second branch to the third was also 45 centimeters and 45 centimeters to the fourth the fifth.