The Fibonacci Sequence - the bridge between Math, Nature, and Art

A look into the Fibonacci Sequence, the Golden Ratio, and their connections to nature and technology

The Fibonacci sequence is a clever mathematical series connected to Nature and the Golden Ratio. The Fibonacci sequence starts with the terms 0 and 1 and follows a specific pattern.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, . . .

If you couldn’t figure it out already, every number equals the sum of the previous two numbers. So 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 = 3, and so on. The sequence is aesthetically pleasing since it creates beautiful spirals when graphed:

Fibonacci sequences are also the basis from which the Golden Ratio is derived. The Golden Ratio is about 1.61803398875. . . and is found by dividing a term in the Fibonacci sequence by the previous term. While this produces inaccurate ratios initially, the numbers get closer and closer to this ratio. For example, 13/8 is 1.625, but 4181/2584 is 1.618034…. The ratio has an attractive property that is seemingly beautiful to the human eye. I don’t mean the number is gorgeous, but the proportion just seems nicer than 1.5 or something else.

Sure it looks good, but you might ask about the connections to nature. The Fibonacci sequence is given by the number of petals a flower has. The Fibonacci sequence also describes the pattern that tree branches take when growing. There are many more, but I would go outside and look for them - it is more fun to find the pattern in nature yourself.

The Fibonacci sequence is also widely used in engineering applications. The pattern is used for data structures, sorting algorithms, audio compression, architectural engineering, and many more.

There doesn’t seem to be a definitive reason why this simple sequence matches the world so well. Still, it is definitively a bridge between math and nature.

Credits:

Image 1: Smithsonian Magazine, Wiki commons: https://www.smithsonianmag.com/science-nature/fibonacci-sequence-stock-market-180974487/

Image 2: Cleveland Design: https://www.smithsonianmag.com/science-nature/fibonacci-sequence-stock-market-180974487/

Further research into the Golden Ratio and it’s applications: https://www.canva.com/learn/what-is-the-golden-ratio/