Nature and The Golden Ratio

We often hear people ask: “Why do we have to take math? We will never use it again.” The fact of the matter is math is all around, wherever we look. Even when you are camping up in the mountains, you can find something that is related to math. In the mountains, nature has made the golden ratio very prevalent in flowers and pinecones.

What is the golden ratio? On the website Live Science, the author Elaine J. Hom described it as the following: “The Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.” What this is saying in an equation is a/b=(a+b)/a= 1.61803398874989…(ect.). This is also referred to the as phi, and it is an irrational number. This is how the ratio would be represented:


An important sequence is introduced when we are talking about the golden ratio. This sequence is called the Fibonacci sequence: 0,1,1,2,3,5,8,13… Each term is the sum in the two previous terms. The more you go to the right of the sequence the ratio of two terms right next to each other it will get closer to the Golden Ratio.

Now you might be asking yourself, “What does this all have to do with nature?” It has everything to do with nature. Let’s look at plants first. Usually, the number of leaves on the plant’s stem is arranged in a spiral pattern permitting the amount of sunlight the leaves need. The way the leaves or petals are arranged the Golden Ratio gives the ideal gap between the leaves or petals and they usually end up being a Fibonacci number. When we look at petals, we notice that they too have Fibonacci arrangements because when looking at them you will see a  pattern. Each of these patterns you will see on petals of a flower all represent the Golden Ratio in their own way.

Looking at the pine cone you will notice the spiral that it naturally takes. Image: Böhringer Friedrich, via Wikimedia Commons.

Looking at the pine cone you will notice the spiral that it naturally takes. Image: Böhringer Friedrich, via Wikimedia Commons.

Just like the petals and the leaves, pinecones are also in a spiral shape. Therefore, they too have Fibonacci qualities. They have two sets of spirals, one going in the clockwise direction and one going in counter clockwise direction, as you can see in the picture to the left. The numbers of spirals in the pinecones are almost always consecutive Fibonacci numbers. For example, there can be 8 spirals clockwise and 5 spirals counter clockwise. This shows the pinecones are related to the rational approximation of the Golden ratio (8/5).

Math is everywhere in our daily life. The Golden Ratio cannot only be seen in nature but it can be seen in everything around us. The Golden Ratio works hand in hand with the Fibonacci sequence.  The more to the right we go in a Fibonacci sequence the more we can relate it back to the Golden Ratio. If we would just take a minute and look around, we will see that math is important and relevant in our daily lives.

For more information about nature, the Golden Ratio and Fibonacci watch this really interesting and quick video  from Vi Hart.


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