Math AA HL IA

Introduction

I have heard the word “Fibonacci” and “Golden ratio” often in my life. However, I was lazy and didn’t look deep into what it was. Before the exploration, I watched some simple explanation video about the Fibonacci sequence and golden ratio on YouTube. The concept of the Fibonacci sequence and golden ratio was amazing and simple than I thought before. I remembered an article I saw somewhere which was “In mathematics, the problem of having the simplest and most profound theory is the best problem and is the subject of pursuing the beauty of mathematics”. Then I thought exploring the Fibonacci sequence and golden ratio would be appropriate for my math exploration and it will be a good opportunity to solve my long curiosity.

The Fibonacci sequence and golden ratio were so much more widely spread in real life than I thought. Such as petals on flowers, organs of the human body, music, spiral galaxies are well- known to the public. My goal of this exploration is to explore the mathematics behind the Fibonacci sequence and the golden ratio which have an intimate relationship between them. Therefore, I will find the function which defines the Fibonacci sequence and check the availability of the function by the mathematical induction. I would investigate further inquiry on the golden ratios between the Fibonacci numbers and even link it to the Fibonacci sequences to apply in the real world.

In further investigation, I will explore the Fibonacci sequence by combining it with my dream of working in the stock market. I will research the Elliott wave principle1 which is used in the financial market. Therefore, I would try out finding the Fibonacci sequence in a dynamic changing stock market and predict the future market trend…