Leonardo Fibonacci. made his entrance into the world around He was born in the humble city of Pisa, Italy

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1 John Townsend Dr. Shanyu Ji Math October 2017 Leonardo Fibonacci Regarded as one of the greatest mathematician of the Middle Ages, Leonardo Pisano made his entrance into the world around He was born in the humble city of Pisa, Italy midway through the Medieval age. The European Medieval world had not developed mathematically, because of their focus mainly on philosophy and literature. They utilized the outdated Roman numeral system, an abacus based off Roman and Greek influences, and their math did not develop past ancient Greek mathematicians discoveries such as Euclid. Medieval Europe was in desperate need for a change. Leonardo s father, Guglielmo Bonacci, made a living as a customs officer in the Algerian city of Bejaia. Formerly, he was a wealthy merchant in the town of Pisa. The small town hosted numerous Moors, one of which took on the task of educating young Leonardo Pisano. Because of the prime location Bejaia was situated on, Leonardo was able to extensively travel the Mediterranean Sea and the adjacent countries such as Egypt, Sicily, France and other surrounding entities. Through his travels, he was exposed to numerous mathematical styles, yet he found the Arabic and Hindi form of mathematics to reign dominant. Introducing this new form of mathematics to Europe, Leonardo completed his Book of Calculating in 1202 entitled, Liber Abbaci. In his book, he begins with fundamentals inherent of

2 mathematics such as, adding, subtracting, multiplying, and dividing. The discrepancy within Roman numeral mathematics was thirteen could be written as XIII, IIIX, or IIXI. Fibonacci s book aims to allow numbers a place, order mattered. Subtraction, in the Roman Numeral system, took more time to interpret. The Romans aimed to take a unit of one, ten, or one hundred and subtract such to obtain the next larger multiple of ten. Leaonardo Fibonacci did not stop at simple mathematical derivations of addition, subtraction, multiplication, and division, but continued in his mathematical endeavors and quest for modernizing Medieval Europe s knowledge. In his book Liber Abaci, in chapter twelve, Leonardo poses the question, How many pairs of rabbits are created by one pair in one year? To explain, he begins with the above written pair bearing in the first month so there will be a total of two pairs in one month, next, one of the two pairs bears in the second month, thus there are three pairs in two months. Two of the pairs are grown and bear in the third month, now pairs of rabbits are born. Thus, there are five pairs in the month. He continues with the algorithm all the way to the fourteenth sequence of numbers because he accounts for the first pair needing to mature to the age of mating. His findings yield three hundred and seventy-seven pairs of rabbits in one year. From this question, Leonardo left the world with a mathematical sequence that would soon be called, Fibonacci sequence/numbers. This extraordinary, ordered sequence is obtained by taking the sum of the two preceding numbers. From this algorithm, we begin to form the sequence 1, 1, 2, 3, 5, 8, 13, etcetra. When

drawn on a graph using rectangles corresponding in area to their Fibonacci number, you can plot and trace a graph that represents numerous natural phenomena.

Fibonacci sequences are seen throughout nature such as wave patterns, hurricane formations, and galaxies can be described in the same manner as the graph of the Fibonacci sequence.

3 drawn on a graph using rectangles corresponding in area to their Fibonacci number, you can plot and trace a graph that represents numerous natural phenomena. This Golden Rectangle once divided can be cut by a transverse arc, which when connected, presents the Golden Spiral. Fibonacci sequences are seen throughout nature such as wave patterns, hurricane formations, and galaxies can be described in the same manner as the graph of the Fibonacci sequence. Observing everyday plants that display the Fibonacci Golden Spiral; the pine cone, the pineapple, artichokes, and cauliflower all grow their fruitlets in such a manner. Turning to floral design, you can always predict the amount of seeds a sunflower will have because they produce seeds in Fibonacci numbers, thirty-four or fifty-five. The nautilus shell is arranged also in the Golden Spiral. The body of a dolphin is arranged in Golden sections with the thickness of the dolphin s tail section corresponding to the same golden section of the from head to tail. Due to Leonardo Pisano of Pisa, Italy, the European Medieval world was able to break through the veil of mathematical darkness, further the quest for mathematical knowledge, and

4 produce some of the greatest mathematicians ever known; such mathematicians as Gottfried Leibniz, Rene Descartes, and Isaac Newton, who owe their discoveries to the inspiration Leonardo Pisano provided. Because of his pioneering efforts on behalf of mathematics, the modern world has been able to observe natural phenomena and be able to come closer to further understanding and knowledge of the world we live in.

5 Bibliography Eves, Howard. Dolciani Mathematical Expositions : Great Moments in Mathematics (Before 1650). Washington, US: Mathematical Association of America, ProQuest ebrary. Knott, Ron. Contents of This Page. Who Was Fibonacci?, 11 Mar. 1998, Thomas, Rachel. The Fibonacci Sequence: A Brief Introduction. Plus Magazine, 6 Jan. 2015, plus.maths.org/content/fibonacci-sequence-brief-introduction. Understanding The Fibonacci Sequence & Golden Ratio. Why Don't You Try This, Fractal Enlghtenment, 27 May 2014, -fibonacci-sequence-and-golden-ratio.html.

Ratio by Using Coefficients of Fibonacci Sequence

International J.Math. Combin. Vol.3(2013), 96-103 Ratio by Using Coefficients of Fibonacci Sequence Megha Garg and Pertik Garg (Punjab Technical University, Jalanahar, Punjab) Ravinder Kumar (Bhai Gurdas