Fibonacci Sequence & Golden Ratio: Math in Nature
- Jeremy Negrin
- Jan 23, 2024
- 2 min read
You always hear people say “Math is boring” or “What is the point of Math?” You do not have to love or hate Math to appreciate it. Simply put, Math is the science of structure, order, and relation used to make sense of the world around us. If you have ever marveled at nature, then you can at least appreciate Math because there might be some sort of grand design…
Leonardo Bonacci (Fibonacci), 1170–1250, was an Italian mathematician who was studying the growth of the rabbit population and asked the following question: “How many pairs of rabbits will one pair produce in one year, given that naturally they produce a new pair every month?”
From his observations, Bonacci came up with the Fibonacci sequence, which is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …, etc. It is a simple, math sequence in which each number is the sum of the previous two numbers, starting at 2. The picture below shows this sequence in the formation of tree branches.
The Fibonacci sequence is significant because of its connection to the Golden Ratio, 1.618033988749894. Two quantities a and b are said to be in the Golden Ratio if
where a < b < 0. The exact value of the ratio is expressed as the Greek Letter φ (phi),
Notice how the Fibonacci numbers perfectly fit into the Golden Ratio in the schematic below, which forms the Golden rectangle, starting with numbers 1 and 1. A square of side length 2 (sum of 1 and 1) is added to form another rectangle, maintaining the Golden Ratio of a + b and a as each rectangle’s longer side and shorter side, respectively (see image below). From such observation, smart mathematicians were able to draw a logarithmic spiral through each square to form the Golden spiral. How golden!
Spirals in Nature
Enough with the math. Here comes the cool part!
If the Golden Ratio is applied as a growth factor in some math equation, we would get a logarithmic spiral — the Golden spiral. Interestingly, this can be found throughout nature. Here are some examples:
The Golden ratio and spiral can be traced in a human face and ear.
“Everything in the universe is within you.” — Rumi
It is important to note that these are approximate calculations of the Golden spiral being applied to natural phenomena. Whether you are a believer or non-believer, the patterns appear frequently enough that its significance cannot be understated.
The Fibonacci sequence and Golden Ratio has captivated mathematicians, artists, designers, and scientists for a long time. Despite the chaotic nature of the universe, this suggests an important characteristic of how nature follows some sort of a blueprint in the grand design of physical matter and attempts to organize it in the most efficient way possible.
What do you think, random or not?
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