**The Fibonacci Sequence in Nature and the Golden Ratio**

by Owen Borville

August 15, 2021

The Fibonacci sequence forms a series of numbers that represent a spiral pattern that is found in nature in many places.

Patterns in nature include spiral, meander, explosion, packing and branching.

The sequence is associated with the golden ratio (phi) and is often called the Divine Proportion, the most beautiful number in the universe.

Tree branch patterns, hurricane spirals, seashell spirals, flower petals, flower heads, the spiral aloe, pine cone heads, galaxies, the human ear, face, hands, DNA structure patterns, and the chicken egg have all been identified as displaying the Fibonacci sequence in their forms.

In addition the mathematical series:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

Discovered by the Italian mathematician Leonardo Fibonacci (1170-1250), the most known mathematician of the Middle Ages, the pattern is shown such that each term in the sequence is the sum of its two preceding consecutive terms.

In addition, if any term in the sequence greater than 2 is divided by the preceding term, the ratio is 1.618.

After the 13th term in the sequence (89/55), this pattern always ends in the ratio 1.618.

**a + b = is to a as a is to b**

The Fibonacci Sequence is also found in Pascal's Triangle, as the diagonal number rows in the triangle sum to this mathematical sequence.

The Fibonacci Sequence is also found in Pascal's Triangle, as the diagonal number rows in the triangle sum to this mathematical sequence.