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Chapter 2 Fibonacci Numbers - MathWorks

Chapter 2 Fibonacci NumbersFibonacci Numbers introduce vectors, functions and Pisano Fibonacci was born around 1170 and died around 1250 inPisa in what is now Italy. He traveled extensively in Europe and Northern wrote several mathematical texts that, among other things, introduced Europeto the Hindu-Arabic notation for Numbers . Even though his books had to be tran-scribed by hand, they were widely circulated. In his best known book,Liber Abaci,published in 1202, he posed the following problem:A man puts a pair of rabbits in a place surrounded on all sides by a many pairs of rabbits can be produced from that pair in a year if itis supposed that every month each pair begets a new pair which from thesecond month on becomes productive?

6 Chapter 2. Fibonacci Numbers You can see that there are n-1 plus signs and n-1 pairs of matching parentheses. Let ϕn denote the continued fraction truncated after n terms. ϕn is a rational approximation to ϕ.Let’s express ϕn as a conventional fracton, the ratio of two integers

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