The Fibonacci Number Sequence and the Golden Ratio: Cosmic Mysteries or Mere Coincidence?

This series of numbers appears in every place: in nature and also from artificial products, from the universe to the classical music.

African numbers ((Φ, φ)), Fibonacci numbers, golden ratios are very well-known and familiar concepts, studied by mathematicians throughout history, from the first time it appeared. It is an infinite sequence of natural numbers beginning with two elements 0 and 1 or 1 and 1, the elements are then set by rules each element is always equal to the sum of two elements before it.

Even contrary to the mathematical stereotype that is dry, the concept of Fibonacci numbers appears in countless other areas such as art, biology, architecture, music, botany and even, finance. Chances are, you have been exposed to the Fibonacci number somewhere in your studies and research career. Does its nature come with the meaning: Can we find a translation written in the number of everything we see, we hear – everything around us?

Perhaps the closest answer to this question is the saying of the great philosopher Plato, ‘ God uses the relentless geometry – God geometrizes continiually’ . Sorry if my limited ability cannot translate a better sentence.


Now take a closer look at the mathematical phenomenon that attracts thousands of intellectuals and scholars from all disciplines, every era since it was first discovered: so is it the golden ratio or the symmetry of god? St?. Before starting this journey, let’s turn to the story of the Italian mathematician Leornardo Bigollo (Leonardo Pisano or ‘who comes from Pisa’), Mr. Fibonacci.

Fibonacci spiral

The African number is called Phi because it is named after the famous Greek sculptor Phidias (who lived in the 5th century BC). He is the creator of famous buildings, including the Parthenon temple in Athens. Teho as Mario Livio wrote in the book The Golden Ratio: The Story of Africa, The World’s Most Wonderful Number, many historians believe that Phidias has successfully applied the golden ratio to his works. .


That’s why mathematician Mark Barr decided to honor Phidias by naming the symbol Φ as Africa. Therefore, Phi is not a discovery discovered by Fibonacci (it has been studied and defined by Euclid already) and the African name does not carry any “Italian flavor” (spaghetti? ).

However, we still need to learn more about Fibonacci’s discoveries to better understand the great balancing potential of African numbers and the numbers generated from it. Fibonacci’s success and the golden ratio figure are two sides of the same coin.

The Fibonacci number sequence is discovered by ‘mathematician from Pisa’ – ranges 0, 1, 1, 2, 3, 5, 8, 13 . – in the field of arithmetic, the industry studies numbers and The fundamental changes that can be made with those numbers The golden ratio, represented by the African name (with the symbol Φ, φ) comes from a success in arithmetic, expressing the relationship. The system of two elements is on a straight line: True, African has a geometric structure as shown below:

We use algebra to find the numerical value of Phi (Φ), we use a simple formula of Φ = a / b. We apply this formula to represent the geometry of the image above, when taking the total length of the segment (a + b) divided by the longer segment (a), we also get the same result when taking the longer segment ( a) divided by shorter paragraphs (b). In summary, we have Phi (Φ) = (a + b) / a = a / b .

The result of this equation is 1.6180339887 ., the same value as the golden ratio defined by mathematician Euclid, under the description of Mario Livio as ‘an infinite number and not repeated’.

Curiously, this number is very similar to the result when dividing any consecutive number in the Fibonacci sequence for each other (eg 5/3 = 1,666; 13/8 = 1,625). Combining these two elements, we succeeded in using geometry to represent an arithmetic category.

This is the point of making this article interesting, not needing a mathematician to be able to understand and see the beauty of algebra. Moreover, we understand more about the basic arithmetic nature of the discovery of the mathematician from Pisa: the famous Fibonnaci spiral.

Is the balance of nature, the science of numbers or just a coincidence?

The characteristics of African numbers surprised us very much, and the discovery of it in the form of golden proportions gave us a way to analyze patterns, objects, geometric representations and even are movements in nature that still take place in this world. It comes up with a saying that was raised somewhere in this article: the golden ratio or divine symmetry .

In the above images, we see the Fibonacci spiral, the rectangle with the golden ratio, but in addition, it can also be used to determine the triangle of golden or pentagonal proportions. But they all have one thing in common: they all have ‘golden elements’ in them.

Pentagon shape with golden ratio.

Some of these golden ratios are self-made, is the environment around us ‘that’ or ‘god’? The buildings with golden ratio are self-made, does Mother Nature apply that formula in creating?

The answer is yes. We can see the golden ratio in the Giza Pyramid in Egypt, in the Google logo, or in rose petals and even, in the shape of galaxies. In La Gioconda – another name for the Mona Lisa painted by Leonardo da Vinci, in the microscopic structure of some crystals, and even (second time), even in the music version Dialogue du vent et la mer of composer Claude Debussy – Fibonacci number sequence appears 50 bar music, can be divided into long sections 21, 8, 8, 5, and 13 bar.

The golden ratio of La Gioconda.

The golden ratio of the galaxy.

The appearance of the number sequence, of this magical golden ratio in every place. So we call it the most interesting number in the world, is it worthy enough? Based on this number, can we change the reality to do the utopian, create a non-math world? But without a doubt, these facts show that math makes us feel that things seem to have nothing to do with each other that have one thing in common: a series of numbers keeps them.

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