Is there some kind of magic formula for the universe?Maybe not, but in nature we repeatedly find some**very general rule**. For example,**Fibonacci Sequence**. This is a series of increasing numbers, where each number (Fibonacci number) is the sum of the two preceding numbers. (We’ll go into more detail about this math later.)

**Fibonacci numbers also apply in nature**as a proportion, it reflects many patterns in nature – such as the near-perfect spiral of a nautilus shell, and the daunting swirl of a hurricane.

Humanity may have understood the Fibonacci sequence**thousands of years** – The mathematical concept of this interesting pattern can be traced back to ancient Sanskrit texts from 600 to 800 BC. But in modern times, we associate it with all kinds of things: a medieval man's obsession with rabbits, computer science, even sunflower seeds.

## 1. Fibonacci numbers and how rabbits reproduce

1202, Italian mathematician**Leonardo Pisano**(Also known as Leonardo Fibonacci, meaning “Son of Bonacci”) Want to know**How many baby rabbits can a pair of male and female rabbits produce?**. Rather, Fibonacci asked the question: How many pairs of rabbits can one pair of rabbits produce in one year? This thought experiment assumes that female rabbits always give birth to pairs of rabbits, and that each pair consists of a male rabbit and a female rabbit.

Picture this: two newborn rabbits are placed in an enclosed area and then begin to reproduce like older rabbits. Rabbits must be at least one month old to be fertile, so during the first month, there are only one pair of rabbits. By the end of the second month, the female rabbit gives birth to a new pair of rabbits, making two pairs in total.

By the third month, the original pair of rabbits gave birth to another pair of newborns, and their previous offspring had grown into large, fertile rabbits. This leaves three pairs of rabbits, two of which will give birth to two new pairs next month, for a total of five pairs.

So how many rabbits will there be in total after one year? This is where mathematical formulas come into play. Although it sounds complicated, it's actually very simple.

The first few numbers of the Fibonacci sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and then increases to infinity.

The mathematical formula describing this sequence is this: X_{n+2} =X_{n+1} +X_{n} , basically, every integer is the sum of the previous two numbers. (You can also apply this to negative integers, but we're only talking about positive integers here.)

To get 2, add the two numbers before it (1+1) To get 3, add the two numbers before it (1+2)

**This set of infinitely summed numbers is called the Fibonacci sequence or Fibonacci sequence**. The ratio between numbers in the Fibonacci sequence (1.6180339887498948482…) is often called the golden ratio or golden number. The ratio of consecutive Fibonacci numbers approaches the golden ratio as the numbers approach infinity.

Want to see how these fascinating numbers appear in nature? You don't need to go to your local pet store; instead, you just need to look around.

## 2. How the Fibonacci Sequence works in nature

Although some**Plant seeds, petals, branches, etc. follow the Fibonacci sequence**, but this does not mean that the growth of everything in nature follows this law. Just because a set of numbers can be applied to a surprising variety of objects doesn't mean those numbers have any relevance to the real world.

Like number superstitions, such as famous people dying in groups of three, sometimes coincidences are just coincidences.

However, while some would argue that the ubiquity of consecutive Fibonacci numbers in nature is overstated, they occur frequently enough to prove that they reflect patterns that exist in nature. You can spot these patterns by observing the way various plants grow. Here are a few examples:

## Seed tops, pine cones, fruits and vegetables

**Observe the arrangement of seeds in the center of a sunflower**you will find that they present a**golden spiral shape**.Amazingly, if you count these spirals, the total will be one**Fibonacci numbers**. Divide the spiral into a left-handed spiral and a right-handed spiral, and you will find that the numbers of the left-handed and right-handed spirals are exactly two adjacent numbers in the Fibonacci sequence.

You can find similar spiral patterns in pinecones, pineapples, and cauliflower, which also reflect the Fibonacci sequence in this way.

## flowers and branches

some plants**Shows Fibonacci sequence at its growth point**, where branches form or branch. A tree trunk grows until it produces a branch, forming two growing points. The main trunk then produces another branch, resulting in three growing points. Then, the main trunk and the first branch create two more growth points, giving a total of five growth points. This continuous pattern follows the Fibonacci sequence.

Furthermore, if you count the number of petals on a flower, you will usually find that the total number is a number in the Fibonacci sequence. For example, lilies and iris have three petals, buttercups and wild roses have five petals, delphiniums have eight petals, and so on.

## bee

A bee colony consists of a queen bee, several drone bees, and many worker bees. Female bees (queen and worker bees) have one pair of parents: a drone and a queen. Drones, on the other hand, only hatch from unfertilized eggs. This means they only have one mother. therefore,**Fibonacci numbers can represent a drone family tree**that is, it has one mother, two grandparents, three great-grandparents (grandmother has two parents, grandfather has only one mother) and so on.

## storm

picture**Storm systems like hurricanes and tornadoes often follow the Fibonacci sequence**. The next time you see a hurricane circling on your weather radar, watch for an obvious Fibonacci spiral in the clouds on your screen.

## human body

Take a good look at yourself in front of the mirror.you will notice your**Most body parts follow the numbers one, two, three and five**. You have a nose, two eyes, three segments on each limb, and five fingers on each hand. The proportions and measurements of the human body can also be divided using the golden ratio. The DNA molecule also follows this sequence, with each double helix period being 34 Angstroms long and 21 Angstroms wide.

Why do so many patterns in nature reflect the Fibonacci sequence? Scientists have explored this question for centuries. In some cases,**This correlation may just be a coincidence**. In other cases, this ratio exists because this particular growth pattern is the most efficient. In plants, this might mean maximum exposure of light-loving foliage or maximum space utilization for seed arrangements.

## Misunderstandings about the golden section

Although experts agree**Fibonacci numbers are common in nature**, but there is more controversy as to whether the Fibonacci sequence is expressed in certain examples of art and architecture. Although some books claimed that the Great Pyramid and the Parthenon (as well as certain paintings by Leonardo da Vinci) were designed according to the golden ratio, upon examination this was found to be false.

Mathematician George Markowski pointed out that both the Parthenon and the Great Pyramid have parts that do not conform to the golden ratio, which is overlooked by those eager to prove that Fibonacci numbers exist in everything. In ancient times, the term “golden mean” was used to refer to something that avoided extremes in either direction. Some people confuse the golden mean with the golden ratio, which is a newer term that only appeared in the 19th century. .

## get something interesting

November 23rd was established as Fibonacci Day, not only to commemorate the forgotten mathematical genius Leonardo Fibonacci, but also because when the date is written as 11/23, four numbers form a Fibonacci That sequence of numbers. Leonardo Fibonacci is also widely credited with being one of the people who moved us from Roman numerals to the Arabic numerals we use today.

Author: Robert Lamb & Jesslyn Shields

Translation: Meyare

Reviewer: Xiaoxian

Original link:Why Does the Fibonacci Sequence Appear So Often?