Fibonacci Sequence: a serie created by nature

The Fibonacci Sequence is found in the nature and in movies like the Da Vinci Code.

The first thing is to enter the two first numbers of it, which are 0 and 1.

fibonacci sequence

Then the series is made like this. The item n equal to the sum of the item N-1 and the item N-2 (or basically the sum of the 2 previous items)

fibonacci sequence

Then select the cell 3 and slide it to the bottom.

drag serie down

And here is the Fibonacci sequence.

fibonacci sequence


Here a graphical representation a the spiral that can be generated. Only the circle center are drawn on a scatter chart. You could use these and then add the circle.

We just superpose the spiral to check the correctness.

fibonacci spiral

Download the files here for excel 2013 or 365 and download it here for previous versions.

And the application in nature are for example (this is from wikipedia):   the branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone,and the family tree of honeybees.

Fibonacci ratios approximate the golden angle, 137.508°.

From the point of view of physics, spirals are lowest-energy configurations which emerge spontaneously through processes in dynamic systems. (wikipedia)