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Home , Fibonacci

The Greatest Mathematician of the

Leonardo Bonacci was an Italian mathematician and author that lived during the Middle

Ages (5th to 15th century in Europe). Bonacci is known to most simply as Fibonacci and the

Fibonacci sequence and other associated terms are accredited to him and his works. One of his greatest achievements was his successful introduction of the Hindu-Arab ic system into the European scientific community. This milestone achievement helped to progress European

out of relying on the outdated and inefficient Roman numeral system and into a

system that is still used today. [7] The publication of his book , meaning Book of the

Abacus, details his worldly studies of from all around the world and was the first introduction of the Fibonacci sequence to the Western world of his time and gave the world a groundbreaking method of connecting mathematics and nature. [2][3] Although very little is known about the true nature of Fibonacci, like many mathematicians before him, the lasting conclusio ns from his life-long works continue to help humans gain a better understanding of the natural world around us.

Born around 1170 in , , Fibonacci was raised in a wealthy family to a father who was a successful merchant. Fibonacci’s father would include him on his travels which led to his exposure to the Hundu-Arabic numeral system. It was not until around the year 1202 that

Fibonacci was able to complete Liber Abaci, a book that summarized the numeral systems already in place in the Old World of the time. Through his travels Fibonacci had seen the benefits of using this numeral system for business around the world but probably did not know that the introduction of such methods would help to propel Europe into economic prosperity. [7][1]

Although Fibonnaci is accredited with other writings, Liber Abaci is the most well-known and provides us with the most significant impact on mathematics. In addition, before Fibonacci

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released the Liber Abaci the European scientific community had no need for a value represented

by 0. Fibonacci wrote of the, “9 figure of the Indians: 9 8 7 6 5 4 3 2 1… and with the sign 0…

any number can be written”. [4] This alone may have been a foreign-enough of a concept to

Middle Ages Europe but the subtle scientific revolution created by Fibonacci did not stop there.

An illustration of the golden spiral created by connecting opposite corners of squares in the Fibonacci sequence. [6]

As mentioned earlier, the Fibonacci sequence is probably the most impactful piece of work attributed to Fibonacci. Although much of what Fibonacci wrote about was already in use in other parts of the world he was the one who took the time out to draft a comprehensive and cohesive book about methods of arithmetic and basic for the rest of the world to learn from. For example, it is now known that the Fibonacci sequence was described by Indian scholars as Virahanka . [8] In short, the Fibonacci sequence is a rule that is dictated by

[6] the formula : Xn = Xn-1 + Xn-2 starting with n=0 and ending indefinitely. Fibonacci was also incredibly fascinated with the fact that when you stack squares with widths corresponding to the

Fibonacci numbers you begin to create a spiral when connecting opposite corners of these squares (illustrated above). Although he did not create these methods, Fibonacci allowed the

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Western world the chance to incorporate his skillset into an evolving scientific world thousands

of miles away from the sequence’s origin. [6]

Truly fascinating is the fact that Fibonacci numbers and the sequence are evident in nature as well. For example, when a plant begins to flower, the arrangement made by the flowers as they exit the stem obey the “Golden Rule”. Phyllotaxis, or the biological study of the arrangement of leaves on a stem, reveals the “Golden” nature of plants. When one divides a circle into, “Golden proportions, where the ratio of the arc length are equal to the , we find the angle of the arcs to be 137.5 degrees.” [2] The bizarre part is that 137.5 degrees is the same angle at which leaves are positioned around their mother stem which allows for maxima l sunlight efficiency and growth ability. Fibonacci’s spiral is also seen in the growth patterns of

certain rose plants where the petals develop according to the Golden pattern. In my opinion it is the greatest achievement for a mathematician to extrapolate such mathematical concepts to the world in which we all exist in and to show that nature is ruled by mathematical phenomena. [2]

Furthermore, the concept of the Golden Ratio, represented by the Greek letter phi, means that, “the ratio of two numbers is the same as the ratio of their sum to the larger of the two quantities. ” The value of the golden ratio is approximately 1.618033. What is the importance and relevance of this ratio to the works of Fibonacci? The answer is simple: we see an incredibly similar value in the ratio of any two successive Fibonacci numbers. In addition, as the Fibonacci numbers we take the ratio of get bigger the value of that ratio continues to get closer and closer to the true value of the golden ratio. Although the golden ratio is an , much like that of , we can say with confidence that there is an unmistakable correlation at play. [4][6]

Like many great mathematicians before him, Fibonacci took the works and teachings of his predecessors and compiled them into a well thought out and easy to follow system. We have

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already seen that Fibonacci took what he learned from the Indians during his travels and used it

to expand the breadth of scientific knowledge in Europe. In addition, and although he may not

have known it, Fibonacci’s teachings and writings helped to transform and increase the prosperity of trade, banking, industry and everyday life. Fibonacci’s ability to clearly see the

Hindu-Arabic decimal system as superior to all others in place during his time resulted in the

scientific accreditations his name enjoys today. Furthermore Fibonacci’s dedication to his studies

resulted in his posthumously adopted title of “The greatest European mathematician of the

Middle Ages” and “The most talented Western mathematician of the Middle Ages” two titles anyone would be happy with being attributed to them. [4][5]

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References

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1 Chandra, Pravin and Weisstein, Eric W. "." From MathWorld--A Wolfram

Web Resource. http://mathworld.wolfram.com/FibonacciNumber.html

2 Parveen, Nikhat. "Fibonacci in Nature." Fibonacci in Nature. University of Georgia. Web. 07

Oct. 2016.

3 Gies, Frances C. "Leonardo Pisano." Encyclopedia Britannica Online. Encyclopedia Britannica.

Web. 06 Oct. 2016.

4 Nikhat, Parveen. "Leonardo Pisano." Leonardo Pisano. University of Georgia, n.d. Web. 07

Oct. 2016.

5 O'Neill, Christopher. "Fibonacci." Fibonacci. Rutgers University, n.d. Web. 07 Oct. 2016.

6 "Fibonacci Sequence." Fibonacci Sequence. Math Is Fun, n.d. Web. 08 Oct. 2016.

7 Dr R Knott: Fibandphi (AT) Ronknott DOT Com. "Who Was Fibonacci?"Who Was

Fibonacci? University of Surrey, 11 Mar. 1998. Web. 08 Oct. 2016.

8 Singh, Parmanand (1985), "The So-called Fibonacci numbers in ancient and medieva l

India", Historia Mathematica, 12 (3): 229–44,

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