The Fibonacci sequence is a famous series of numbers with a pattern. The pattern is that every number is added to the one before it. Here are the first few parts of the sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
As you can see, 1 + 1 = 2, 2 + 1 = 3, 3 + 2 = 5 and so on. It’s a really simple progression and can go on forever. What’s impressive about this sequence is that you get a spiral if you turn those numbers into boxes. Take a look at the image below as an example:
What is the history of the Fibonacci sequence?
The Fibonacci sequence is like a lot of maths theories. It doesn’t come from a specific place. It was talked about and built upon by lots of different people. But, the earliest mention of it comes from India. It’s mentioned in works by Pingala, an Indian writer, as early as 200 BC.
The sequence was introduced to mathematicians in Western Europe by a man called Leonardo of Pisa. He published a book called Liber Abaci in 1202, discussing the Fibonacci sequence. It is also the reason for its name, as Leonardo of Pisa later became known by Fibonacci.
Fibonacci numbers typically show up unexpectedly. It’s common for them to appear in maths when you don’t expect them to. However, these numbers are so useful that they’ve been applied to many maths methods. For example, there’s the Fibonacci search technique, the Fibonacci heap data structure, and Fibonacci cube graphs.
Where can you see the Fibonacci sequence in real life?
You can see the Fibonacci sequence in many things in real life. But, surprisingly, it’s found a lot in nature. Here’s a list of where you can find the Fibonacci sequence in real life; think about the spiral from earlier and where you might find it.
- Shells: Lots of shells form the spiral seen in the picture above. These can be seashells, snail shells, and nautilus shells. The lines in shells are really clear and easy to see. It makes them one of the best examples of the sequence being found in nature.
- Flowers: If you look closely at the center of some flowers, you can see that they follow the Fibonacci sequence in detail. The flower’s middle bit, which connects all the petals, is called the pistil. It is where you’ll need to look. Rose petals are another great example too. If you look at how the petals spread out from the pistil, you can map the spiral.
- Leaves: Leaves follow the Fibonacci sequence in two ways. The way that they grow from branches and the way their veins behave. The veins inside of the leaves branch off following the series.
- Clouds and storms: If you’ve ever seen pictures of storm clouds, they’re typically in spirals. But if you look closer, you can map the Fibonacci curve onto the clouds. You can best see this with tornadoes and hurricanes.
What is the golden ratio?
If you’re learning about the Fibonacci sequence, you will also learn about the golden ratio. They’re very closely related to each other. So, what is the golden ratio? It’s an impressive number that equals around 1.168. You can find it in a lot of different places too. Art, architecture, geometry, maths, and the human body.
To find the golden ratio, imagine a line. Then divide the line into two parts, but ensure that one part is bigger than the other. Now, divide the long part by the short part. Then, divide the whole length by the long part. You’ve got the golden ratio if these two results are the same. What’s amazing about the golden ratio is that it always remains the same, no matter what numbers you change in the calculation.
How does the golden ratio relate to the Fibonacci sequence?
The golden ratio relates to the Fibonacci sequence amazingly. If you take two consecutive numbers from the series, their ratio is very close to that of the golden ratio. It gets even weirder. The higher the numbers you use from the Fibonacci sequence, the closer it gets to the golden ratio. Nobody knows why this happens, but mathematicians will observe it.