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Fibonacci Numbers

Fibonacci, the person, was actually named Leonardo Pisano but became known as Fibonacci through a mistranslation of his writings, but the name just stuck. It seems he was possibly born 1170 in North Africa. He started his studies with an Arab master but later studied in Egypt, Syria, Greece, Sicily, and Provence. His mathematical book translated to “Book of the Abacus” is one of his great works. However, his claim to fame stems from the Fibonacci numbers.

The infinite series of numbers created by the Fibonacci sequence are as follows...

\(0,1,1,2,3,5,8,13,21,34,...\)

Closed formula for Fibonacci Numbers

\(F_n=\frac{1}{\sqrt{5}}\left(\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{2}\right)^n\right)\)

They are a second-order recurrence.

\(F_n = F_{n-1} + F_{n-2}\)

What is interesting about these Fibonnaci numbers is that they are almost mystical as they show up naturally all over the place.

Here is how these numbers manifest themselves on a shell.

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