There is one thing more painful than learning from mistakes (our own or somebody else's): Not learning from them.  Barbara Johnson 
Biography of FibonacciLeonardo Fibonacci was born in 1170 in Pisa Italy and is sometimes remembered as the "greatest European mathematician of the middle ages." His full name was Leonardo of Pisa, or Leonardo Pisano in Italian, since he was born in Pisa, Italy, yes, the city with the leaning tower. He called himself Fibonacci [pronounced fibonarchee] which is short for filius Bonacci. At the time, Pisa was an important commercial town which traded with many Mediterranean ports. Leonardo's father, Guglielmo Bonacci, was a type of customs officer in the North African town of Bugia now called Bougie. It is believed that Leonardo was given a North African education under the Moors and later traveled extensively around the Mediterranean. It is assumed that Fibonacci died around 1250. During his life, he wrote a number of mathematical texts that were said to revive ancient mathematical skills. Specifically, he is responsible for introducing the decimal numbering system into Europe. This is the modern system of math that uses a ones, tens, and hundreds, etc., position with a decimal point. Prior to that, the Roman numbering system was still being used, which, if you could imagine, was rather more difficult to perform arithmetic. Fibonacci SeriesIn his book about mathematics, Fibonacci included an example whose answer would become the famous Fibonacci Series:
The answer to this riddle is the famous Fibonacci series, which represents the number of rabbits each month. It looks like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, etc. Starting with 1, 1, the next value is simply the addition of the two previous values. This wasn't known as Fibonancci Series until a French mathematician Edouard Lucas (18421891) who found many more applications for it. Golden MeanOne of the rather more interesting aspects of the Fibonacci Series is that it related to the Golden Mean Ratio, or Phi. This ratio is calculated by taking the ratio of one value in the Fibonacci Series as compared to the next, for example 5 to 3 or 8 to 5 or 987 to 610. This ratio approximates phi more and more closely, the farther out you go. It theoretically ends up being exactly equal to the ratio of Phi. Read more about Fibonacci. 

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