Running Head: BONACCI REVOLUTIONIZED THE WORLD 1

Transcription

1 Running Head: BONACCI REVOLUTIONIZED THE WORLD 1 Bonacci Revolutionized the World A Review of the Fibonacci Numbers Sapphire Ortega El Paso Community College Author Note This paper was prepared for Math 1314, taught by Professor Macedo

2 BONACCI REVOLUTIONIZED THE WORLD 2 Abstract Mathematician Bonacci has been a huge part of understanding and revolutionizing the world. Fibonacci numbers are used and seen everywhere. Most people may not know it, but they are there. They are used in the everyday Mc Donald s fast food restaurants when people purchase their food, and surprisingly enough Fibonacci numbers are on the floor tiles too. This goes to show how Fibonacci numbers appear in places people go to everyday. Remember when all through school a math teacher said, Math is everywhere? Well, this paper should make that crystal clear. In this paper one important example of how and why the Fibonacci numbers sequence is important will be introduced, as well as a little bit about mathematician Bonacci s background.

3 BONACCI REVOLUTIONIZED THE WORLD 3 Bonacci Revolutionized the World Most often, certain individuals are not known for having been a part of a huge role on why the world works the way it does. These individuals have discovered the answers to topics most people would never have thought to discover. Their studies have provided many people answers to certain parts of life. There is a certain mathematician the world should thank for how it is not so difficult how numbers are counted, and that is mathematician, Bonacci. Bonacci, was born in Pisa, Italy. Bonacci s original name is Leonardo Pisano. In this paper, he will be referred to as Bonacci. Bonacci, spent a lot of his childhood with his dad in North Africa. While he was there he was educated by the moors and as an adult he later traveled to Egypt, Syria, Greece, Sicily and Provence. In fact, he traveled and learned so much that when returning one day to his hometown Pisa, he began writing his own book, Liber Abaci. This book shined a new light on an important subject well known as the decimal number system today (Knot, 2013). This book was written with all the knowledge he accumulated throughout his time in North Africa from the Hindus which included his main accomplishment, introducing the Hindu-Arabic numerals or as everyone calls it, the decimal number system (Archimedes, 2016). However, before the decimal number system there was a complex and common way of counting with roman numerals. According to Roman Numerals History in Use it states that the, Roman [E]mpire had inspirational developing [sophisticated] intellectual and mathematical skills to build However, their number system was flawed, it had no zero (0), and no single method for counting above several thousand units (Roman Numerals History and Use). The author is showing that the Roman numeral system was not all flawed because it did bring memorable architecture to history, but it did not help when counting to the thousands and farther than that. For example,

4 BONACCI REVOLUTIONIZED THE WORLD 4 many who were in elementary in the 20 th century, in History class, were taught how to use and understand the Roman Numeral System. However, most of those children got confused when working with the beginning numbers such as, I, II, and III. When the numbers started to increase, they would find themselves lost. They may have wondered, How and where did that line come from? This must have proved that if a child can understand how to write 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, then the Roman numeral system must be replaced with the quick and better understood system known as the decimal number system. Therefore, most people count with the decimal number system because it is easier and faster to work with, and more progress can be accomplished with it (refer to appendix A to see a roman numeral chart). Thankfully, Bonacci, introduced the decimal number system first to the Latin-speaking world and in his book, it notes, "These are the nine figures of the Indians: With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written" (Knot, 2013). This piece from his book is showing that instead of having to do things in a complicated way, here you only have ten numbers as opposed to many confusing and time consuming roman numerals. Again, Bonacci did not discover these numbers he was shown these numbers, including the number zero by the Hindus. He then worked from there by writing his book Liber Abaci (Archimedes, 2016). Later, Bonacci also showed the merchants of Italy how simple and fast the decimal number system could be compared to the Roman numerals. Once everyone noticed this new method Bonacci introduced, it became what the world today knows as, the Fibonacci numbers (Knot, 2013). Bonacci has impacted the world in a huge way. If it were not for him there would be a different world, probably not as advanced as today. Bonacci is important because of the Fibonacci numbers. The sequence goes as follows 0, 1, 1, 2, 3, 5, 8 One will notice a pattern looking at the sequence. Knott in another website

5 BONACCI REVOLUTIONIZED THE WORLD 5 shows the pattern is the sum of two numbers before the next result gives the final result. The pattern is infinite. However, going back to the main point here, Bonacci noticed the numbers were in nature. For example, a flower has 5,8, or 13 pedals. This made Bonacci more curious so he started observing everything about nature and realized everything had a rectangle shape with little square Fibonacci number parts with a spiral when observed closely (refer to appendix B to see the figure) (Knot, 2016). This is important because this explained a lot of answers to life. Bonacci noticed that everything such as, pinecones, cabbages, apples, and broccoli had a certain spiral to them and when counted would equal a Fibonacci number. This spiral is known as the golden ratio or golden spiral (Knot, 2103). Did it mean everything had these numbers? The answer is yes. However, this is when the confusion happens. How do plants count? How does nature keep up with these patterns? These questions must have come into mind when Bonacci saw the pattern. Fortunately, scientists existed at the time and could answer the question to that. Now, it was not because plants could count but it had to do with a hormone in the plant. The hormone tells the plant to grow. The plant needs enough room to grow so it moves where a farther hormone is. This causes the plant bit to move and thus many other plant bits do the same. This becomes a pattern and once it is started there is no way to stop it. Therefore, plants and plant leaves are farther apart from each other. It is how they survive with the Golden ratio (Hart, 2012). The golden ratio allows them to get enough sun and not cover each other s leaves for survival (refer to appendix C to see how far apart the plant s leaves grow from each other). In addition to plants having Fibonacci numbers there are other parts of nature that have Fibonacci numbers like every measurement of every animal made by nature, which has the golden ratio when the structure is fully analyzed (refer to appendix D to see a figure of a dolphin

6 BONACCI REVOLUTIONIZED THE WORLD 6 in the golden ratio measurements). Human bones are also Fibonacci numbers (Parveen n.d.). Parveen notes, It is also worthwhile to mention that we have 8 fingers in total, 5 digits on each hand, 3 bones in each finger, 2 bones in 1 thumb, and 1 thumb on each hand. The ratio between the forearm and the hand is the Golden Ratio (Parveen, n.d.). A is below. There are so many other ways Fibonacci numbers are used. It is truly amazing to see how important these numbers are. Surprisingly enough this in not all Fibonacci numbers have done to the world. They have helped shape people and the world how it is today. Some people may not know who Bonacci is, but if it were not for him they would not be working with numbers the way they do now. However, even though he is not well known he is still used in the everyday life and that is something not a lot of people can say they have accomplished. Bonacci will continue to live until the world vanishes.

7 BONACCI REVOLUTIONIZED THE WORLD 7 References Archimedes, A.L. (2016, November 03). Numbers' & Numeral systems history and curiosities. Retrieved from Hart, V.H. (2012, January 20). Doodling in Math: Spirals, Fibonacci, and Being a Plant [Part 3 of 3]. YouTube. Retrieved from video file =loip_z_-0hs&v=14-ndqwkz9w Knott, D.R.K. (2016, September 25) Fibonacci Numbers and Nature. Retrieved from Knott, D.R.K. (2013, November 4). The Life and Numbers of Fibonacci. Plus Magazine. Retrieved from Knott, D.R.K. (2013, November 4). Golden Growth. [photograph] Plus Magazine. Retrieved from Parveen, N.P. (n.d.). Fibonacci in Nature. Retrieved from Parveen, N.P. (n.d.). Fibonacci in Animals. [Diagram]. Retrieved from Roman numerals, R.N. (n.d.). Roman Numerals History and Use. Retrieved from Roman numerals, R.N. (n.d.). Roman Numerals Chart. [chart]. Retrieved from

8 BONACCI REVOLUTIONIZED THE WORLD 8 Appendix A Figure 1 Complex View of Roman Numerals Note. The data on the roman numerals are adapted from

9 BONACCI REVOLUTIONIZED THE WORLD 9 Appendix B Figure 2 The Famous Spiral Note. the figure of the spiral is retrieved from

10 BONACCI REVOLUTIONIZED THE WORLD 10 Appendix C Figure 3 Nature s Pattern Note. the photograph of the pattern of the plant leaves is adapted from

11 BONACCI REVOLUTIONIZED THE WORLD 11 Appendix D Figure 4 Dolphin Structure in the Golden Sections Note. The example that shows that animals also have Fibonacci numbers is adapted from