# The Fibonacci Sequence

**This is an English exploratory essay on the Fibonacci Sequence. Custom research papers are Paper Masters specialty. **The topic is the Fibonacci Sequence.

- You don't need to have an argumentative or definitive thesis.
- You don't even necessarily have to answer your exploratory question.
- You don't really need to have a finite conclusion.
- Sort of goes against everything you've learned up to this point, right? Good.

This paper is about satisfying a genuine curiosity using the research process to explore and the writing process to reflect that exploration.

In this paper, you should:

- Narrate your research process
- integrate the pertinent information that you learn as you explore that topic
- Assimilate that information, tell me how it helps answer your research question, react to it and/or have an opinion about it.

## Here is a good way to attack a research paper on the Fibonacci Sequence:

- Do some listing on potential topics as soon as possible.
- Be sure to look through the sample essays available on Paper Masters.
- Start with a question about your issue, and why you're interested in that question.
- Do some research on that question.
- Write out your process EXACTLY, and step-by-step. (So yes, you'll say: The first thing I did to find information was to set up an interview with the Governor)
- Now your initial research should have led you to more questions. Start following those, and duplicate the process: ask the question, do more research, write about it.
- Now you may come to a point where you've answered your question: that's fine. You can finish up that way, and you might even want to use that conclusion as a starting point for your final argumentative paper.
- But, you don't have to answer everything. The key is to ask good questions and pursue them. If by the end of your paper you just stop, then fine. You can end there without any trite and summative conclusion.

### History of the Fibonacci Number Sequence

The Fibonacci sequence is a series of numbers where the total of two consecutive numbers equal the next number in the series. For instance, 13, 21, 34 is a part of the Fibonacci sequence because 13 plus 21 equals 34. The sequence begins 1, 1, 2, 3, 5. In some instances, the sequence begins with zero.

The Fibonacci sequence was developed in response to one of the mathematical contests that he frequently participated in. One particular contest asked the question, “Beginning with a single pair of rabbits, if every month each productive pair bears a new pair, which becomes productive when they are 1 month old, how many rabbits will there be after n months?” In order to solve this problem, Fibonacci devised a series of numbers in which each number is the sum of the previous two (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... ,). This proved to be the first recorded instance in European scholarship of a recursive number sequence, or one in which the relation between two or more successive terms can be expressed by a formula. Fibonacci numbers can create intricate patterns that reveal order hidden within systems that at first appear disorderly. This has lead some stock traders to use the sequence to find order within evolving stock values. Similar practices have attempted to impose order on chaotic systems with the golden rectangle and golden spiral. In addition to proving useful in the solution of the rabbit problem, this sequence of numbers has come to have numerous other applications in a variety of other fields, shedding light on aspects of calculations dealing with processes including computers, finance banking, fractals, and biological models.

Today, there is an academic journal, *The Fibonacci Quarterly, *which is entirely devoted to the study of theory and applications related to the Fibonacci sequence.

#### Related Innovations and Importance of Fibonacci

The Fibonacci sequence appears in many Sanskrit mathematical writing. The earliest development of the sequence began as a list of long and short syllables. Today, Fibonacci numbers are largely used to predict or recreate natural representations of mathematical ideas. For instance, a shell can have a spiral that resembles a graphed form of the Fibonacci series.

Another of the significant innovations linked to Fibonacci is known as the golden section. This refers to a special value that is closely related to the Fibonacci sequence of numbers. The golden section is also known as the golden mean, the golden ratio, or the golden number. In mathematics, it is often referred to by the Greek letter phi. The golden section refers to a number that can be squared by adding 1. Other ways that this value can be represented are ± 0·61803 39887... and ± 1·61803 39887..., or (1 + SQR(5))/2. Similarly to the Fibonacci sequence, the golden section has proven to have many applications in developing the calculations for current technology and theory.

By developing the Fibonacci sequence and introducing Hindu-Arabic number systems and algebra theory to Europe, Leonardo Fibonacci had a profound and far-reaching effect on the evolution of the study and application of mathematics in Western civilization. If he had not endorsed the incorporation of these elements, the course of Western thought may have been drastically different.