Fibonacci sequence history,mt4 trading platform for blackberry playbook,how to trade penny stocks online,direct access trading brokers list - You Shoud Know

13.03.2014 admin
This author has taken the liberty of directly quoting from some of the references given here, such as the quotations by some scholars or historians and, when necessary actual descriptions of the mathematical notations (rather than paraphrasing them).
The 13th Century Italian Leonardo of Pisa, better known by his nickname Fibonacci, was perhaps the most talented Western mathematician of the Middle Ages. Fibonacci is best known, though, for his introduction into Europe of a particular number sequence, which has since become known as Fibonacci Numbers or the Fibonacci Sequence. The sequence, which had actually been known to Indian mathematicians since the 6th Century, has many interesting mathematical properties, and many of the implications and relationships of the sequence were not discovered until several centuries after Fibonacci's death. It should be remembered, though, that the Fibonacci Sequence was actually only a very minor element in “Liber Abaci” - indeed, the sequence only received Fibonacci's name in 1877 when Eduouard Lucas decided to pay tribute to him by naming the series after him - and that Fibonacci himself was not responsible for identifying any of the interesting mathematical properties of the sequence, its relationship to the Golden Mean and Golden Rectangles and Spirals, etc.


I am indebted to the original authors for their scholarly writings, without which justice could not have been done in narrating the contributions of Indians in Mathematics through history. He discovered the sequence - the first recursive number sequence known in Europe - while considering a practical problem in the “Liber Abaci” involving the growth of a hypothetical population of rabbits based on idealized assumptions. For instance, the sequence regenerates itself in some surprising ways: every third F-number is divisible by 2 (F3 = 2), every fourth F-number is divisible by 3 (F4 = 3), every fifth F-number is divisible by 5 (F5 = 5), every sixth F-number is divisible by 8 (F6 = 8), every seventh F-number is divisible by 13 (F7 = 13), etc. His “Liber Quadratorum” (“The Book of Squares”), for example, is a book on algebra, published in 1225 in which appears a statement of what is now called Fibonacci's identity - sometimes also known as Brahmagupta’s identity after the much earlier Indian mathematician who also came to the same conclusions - that the product of two sums of two squares is itself a sum of two squares e.g. He noted that, after each monthly generation, the number of pairs of rabbits increased from 1 to 2 to 3 to 5 to 8 to 13, etc, and identified how the sequence progressed by adding the previous two terms (in mathematical terms, Fn = Fn-1 + Fn-2), a sequence which could in theory extend indefinitely.


It is also historically important as it is the earliest known text offering a direct treatment of decimal fractions.



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