Milestone Five: Final Paper 1 Milestone Five: Final Paper Jessica Baker MAT 135 – The Heart of Mathematics Instructor: Michael Smith April 21, 2019
Milestone Five: Final Paper 2 Introduction The Fibonacci sequence is not only one of the most famous formulas in mathematics but is also a mathematical phenomenon that has been present well before it was even discovered. It can be described as sequence that exhibits specific numerical patterns and has proven to be far more important than its creator could have ever imagined. In this paper we will review the historical significance of the Fibonacci sequence, discussing who and how the sequence came to be discovered. The next section will explore the mathematics behind the Fibonacci sequence and touch upon its importance to the mathematical world. The final section of this paper on the Fibonacci sequence will highlight real world applications and occurrences that can be found in everyday life and conclude with my personal reflection on this mathematical idea that continues to amaze and mystify those who try to explain the reasoning behind this numerical pattern. Historical Significance The Fibonacci Sequence was developed by a man named Leonardo of Pisa. The name Fibonacci means, “House of Bonacci”. There is not very much known about Leonardo of Pisa, however, it is believed that he was born in 1170 in Pisa, Italy to a merchant father, Guilelmo Bonacci. Being the son of a merchant, Leonardo had the opportunity be around mathematics. When Leonardo was a teenager, his father worked at a customs house on the coast of North Africa (currently Algeria) in which he was exposed to Arabic mathematics. Leonardo would learn the Hindi numerals 1 through 9 and the Arab numeral 0. At this time in history, most of Europe was using Roman numerals, however, Leonardo found the Arabic numerals were easier to work than that of the convoluted Roman numerals system. With the Roman Numerals system, basic calculations were time consuming, which includes using an abacus and then converting to Roman Numerals, also known as the Dark Ages. The Hindi system enabled the user to record
Milestone Five: Final Paper 3 the steps through the process including the final answer. (Bradley, 2006) This background in Arabic mathematics knowledge led to Leonardo’s life work in mathematics as well as paved the way for Europe as a whole to adapt the newer Hindu-Arabic system and to abandon the Roman numeral system. This adaptation, evolved into a wonderful time of intellectual, financial and commercial upswing in Europe. (Devlin, 2011) The first appearance of the Fibonacci sequence was in Indian Mathematics, and specifically in Sankrit Prosody. In Sanskrit there are 2 different sets of syllables, long syllables called guru (“heavy), with two beats of time and short syllables called laghu (“light”) with only one beat of time. Those who studied Sanskrit in Ancient India were interested in calculating all
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