Fibonacci Sequence

(Why 4 leaf clovers are hard to find.)

Consider yourself lucky if you find a four leaf clover because they are rare in nature. In the natural world there are certain patterns of numbers that repeat themselves over and over again, in the way flower petals are attached to a stalk, branches grow from a tree, bracts are arranged on a pine cone, leaves are arranged on a stem, etc. This sequence of numbers was named the Fibonacci sequence in honor of Leonardo Fibonacci an Italian Mathematician who referenced this order of numbers in a book he wrote in 1202. This Fibonacci sequence is often called nature’s numbering system because it is so commonplace. The Fibonacci sequence normally begins at 0 or 1 and the next number corresponds to the sum of the previous two numbers. Example: 0,1,2,3,5,8,13,21,34, 55, 89 etc. This can be illustrated arithmetically by Xn = Xn-1 + X n-2. In nature Fibonacci numbers normally create a spiral shape when they are plotted; and you can often see this shape in the way flower petals, tree limbs, sea shells etc. are arranged. Scientists believe that this radial pattern is the most effective way to organize plant parts to optimize space along a stem and maximize exposure to sunlight, etc., so that plants exhibiting these characteristics would have a competitive advantage over those that do not. Fibonacci numbers repeat themselves in other areas such as mathematics, economics, computer programming, and physics to name a few; and, they are employed in many applications throughout these disciplines. Some stock market analysts go so far as employ Fibonacci numbers to predict how individual stocks and the market in general will behave.

Credit: wikimedia.org - L. Shyamal

Leonardo Fibonacci (1170 -1250) traveled extensively throughout the Mediterranean Region and Middle East during his formative years. As part of his travels he was exposed to the Hindu Arabic numerical system (our present system of numbering 1, 2, 3 etc.) for conducting business and may have learned about repeating sequence of numbers from the ancient journals of Indian Mathematicians. Fibonacci published the book Liber Abaci (Book of Calculations) in 1202 that both detailed the repeating sequence of numbers and explained why the Hindu – Arabic numerical system was easier and more accurate than the Roman Numerical system that was still widely used throughout Europe. This book is cited as one of the leading forces behind Europe’s adoption of the present numbering system and the development of Fibonacci sequence in popular culture. Fibonacci published other important volumes including a journal that employed algebraic methods to solve complex geometrical problems and the use of squares and square roots as part of the numbering system. For all his work Fibonacci is considered to be one of the most influential Mathematicians of the Middle Ages and throughout history. A Stature of Fibonacci was erected in Pisa, Italy in his honor and the date November, 23 (11-23) was set aside to honor this great mathematician.

Article by FCFCDB

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