The Fibonacci Numbers: Part Two – in Nature

Romanesco Broccoli – Exhibits Fractal Behavior & the Fibonacci Sequence – Image by Jon Sullivan, Wikimedia Commons

The Fibonacci sequence of numbers, an infinite series, was defined mathematically, in Part One, to be

Fn = Fn˗₁ + Fn˗₂.

Their sequence begins, 0, 1, 1, 2, 3, 5, 8, 13….

The question arises, how do these numbers manifest themselves in nature, around us? What is their significance, their métier?

Fibonacci on Land

There are numerous manifestations of the Fibonacci sequence in nature. Quite a few are listed at the University of Surrey mathematics web-site. The site explains Fibonacci’s problem of the multiplying rabbits that lead, in the year 1202, to his namesake sequence.

Although the logic behind that problem contains a number of flaws, it did introduce Fibonacci and his sequence to us. A real occurrence of Fibonacci numbers in nature can be seen in the bottom of a pine cone.

Fibonacci in the Sea

Perhaps most inspiring is the occurrence of the Fibonacci numbers is seen in a sea-dwelling creature. The Fibonacci sequence, if visualized as a sequence of squares drawn in clockwise fashion (as in these images) can be seen to form a spiral. Compare that spiral with the cutaway shell of the nautilus.

The concluding, Part Three, of this series of articles will discuss the significance of these occurrences of Fibonacci’s numbers in nature.

References:

  • University of Evansville, Indiana: Fibonacci

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