Deciphering the Fibonacci Sequence

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You may have heard the expression, it’s certainly one of the most famous mathematical concepts – show what’s involved with he Fibonacci Sequence?.

The thirteenth Century Italian Leonardo of Pisa, better known from his nickname Fibonacci, was possibly the most gifted Western mathematician of the Middle Ages. Little is known of his life except that he has been this son of a customs official and, as a young child, he traveled to North Africa along with his father. It was here that he first heard about the Arabian mathematics. On his return to Italy, he helped to spread this knowledge through Europe, putting so in motion a rejuvenation in Western mathematics, which had lain largely dormant for centuries throughout the Dark Ages. Especially memorable was that in 1202 he wrote a very influential book called Liber Abaci, wherein he encouraged using the Hindu Arabic numeral system. Here he used the book to describe its lots of advantages for retailers and mathematicians alike across the clumsy system of Ancient Rome numerals then in use in Europe.

Despite its apparent benefits, uptake of this system in Europe was slow, and Arabic numerals were banned within the town of Florence in 1299 on this pretext they were easier to falsify than Ancient Rome numerals. Yet, common sense finally prevailed and the new system has been adopted through Europe by the fifteenth century, making the Ancient Rome system obsolete. The flat bar notation for fractions was initially first utilized in this work. Fibonacci is best known, however, for his debut in Europe of a certain number sequence, that has since become known like Fibonacci Numbers or this Fibonacci Sequence.

There are lots of explanations of this, which although initially sounding quite complicated is actually very simple. ¬†One of the most straightforward ones I’ve heard is to be found on the BBC’s History of Maths programs – you can access this and any other UK TV abroad, from here.

He discovered this sequence – this first recursive numerical sequence known in Europe – although considering a practical problem in this Liber Abaci involving this growth of a hypothetical population of rabbits based about idealized assumptions. He noted that, after every monthly creation, this number of pairs of rabbits increased from 1 to 2 to 3 to 5 to 8 to 13, etc. Soon he also recognized how a sequence progressed by adding this previous two terms, a sequence which could theoretically extend indefinitely.

The arrangement, which had really been known to Indian mathematicians since this sixth Century, has many intriguing mathematical properties, and a lot of this implications and relationships of this sequence weren’t discovered until several hundreds of years after Fibonacci’s death. For example, this sequence regenerates itself in some surprising ways: every 3rd F number is divisible by 2, every 4th F number is divisible by 3, every 5th F number is divisible by 5, every 6th F number is divisible by 8, every 7th F number is divisible by 13, etc.

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