*THE FIBONACCI SERIES AND ARCADIA*

*(AKA, VALENTINE'S GROSSING OF THE GROUSE!)*

The Fibonacci Series was developed in 1202 by the Italian mathematician Leonardo Fibonacci. He was a prominent mathematician of the Middle Ages, and originally devised the Series as a solution for estimating the population growth of rabbits. Not only did Fibonacci discover the Fibonacci Series, he was also the first European to introduce the Hindu/Arabic number system in Europe. His great contributions to mathematics are recognized around the world, and his memory lives on through mathematical calculations all over the world.

The first few numbers of the Fibonacci Series are:

**1,1,2,3,5,8,13,...**

The process of finding the numbers of the Fibonacci Series is derived from the following formula:

**u(n + 1) = u(n) + u(n - 1)**

Each following number in the Fibonacci Series is found from adding the two previous numbers. Mathematicians were trying to find the ratio between two consecutive numbers in the Fibonacci Series, called the "Golden Ratio." They found the number to be about .6180339887, which is about equal to:

**(1+SQRT 5)/2**

The formula to find a given number in the Fibonacci Series is:

**u(n) = 1/SQRT 5{[(1+SQRT 5)/2]^n-[(1-SQRT 5)/2]^n}**

The Fibonacci Series has been used as an estimate to determine patterns of development and growth in nature, especially for asexual reproduction. For example, the placement of leaves on a garden plant follows the Fibonacci Series. The leaves will grow in a spiral around the stem, with each leaf growing at an exponential rate following the Fibonacci Series. The leaf pattern will repeat itself, with leaf #6 growing directly underneath leaf #1. This pattern of asexual reproduction is defined by the phyllotactic series, which is made up of the Fibonacci Series in both the numerators and denominators. The leaf below is in the 2/5 phyllotaxy.

OK! Now that you are fully aware of the process of the Fibonacci Series and its relation to your everyday life, we're positive you now want to know how the Fibonacci Series relates to Arcadia. The main reference to the Fibonacci Series in Arcadia is Valentine's study of the grouse population in Sidley Park. While working as a graduate student at Oxford University, Valentine attempted to put a model of the pattern of the grouse population. The Fibonacci Series, because of its original use as a estimate for the rabbit population, aided Valentine in his search for the truth of the plight of the grouse on Sidley Park. The Fibonacci Series was used as the starting point for Valentine's discovery that Thomasina began using fractal geometry. The iteration that Thomasina developed while trying to plot the apple leaf, which was later completed by Valentine, uses the basic principles of the Fibonacci Series. The pattern of the leaf was repeated over and over again, just like the Fibonacci Series.

Well, thanks for reading and have a great day! :)

Page by Janet Borth and Casi Clay

For more fun facts on the Fibonacci Series and its uses, visit: the University of Surrey, UK, website on the Fibonacci Series.

*Bibliography: *

*Grolier Electronic Publishing, Inc. Encylopedia Americana ©
1995 *

*Internet: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
*

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