This sequence of numbers appears everywhere: in nature and also from man-made products, from the universe to classical music.
Phi ((Φ,φ) ), Fibonacci number, golden ratio are very famous and familiar concepts, which have been studied by mathematicians throughout history, from the time when it first appeared. It is an infinite sequence of natural numbers starting with two elements 0 and 1 or 1 and 1, the elements of which are then established according to the rule that each element is always equal to the sum of the two preceding it.
Even, contrary to the preconceived notion of arid mathematics, the concept of Fibonacci numbers appears in countless other fields such as art, biology, architecture, music, botany and even finance. Chances are, you’ve come into contact with Fibonacci numbers somewhere in your academic and research career. Does its essence come with the meaning: Can we find a numerical translation of everything we see, we hear – everything around us?
Perhaps the closest answer to this question is the statement of the great philosopher Plato, ” God geometrizes continually” . I’m so sorry if my limited ability can’t translate a better sentence.
Plato.
Now let’s take a closer look at the mathematical phenomenon that has attracted thousands of intellectuals and scholars from every discipline, every era since it was first discovered: is it the golden ratio or the divine symmetry? St?. Before we begin this journey, let’s go back to the story of the Italian mathematician Leornardo Bigollo (Leonardo Pisano or “the man from Pisa”), Mr. Fibonacci.
The number Phi is called Phi because it is named after the famous Greek sculptor Phidias (who lived in the 5th century BC). He was the architect of famous architectural works, including the Parthenon in Athens. Teho as author Mario Livio writes in the book The Golden Ratio: The Story of Phi, The World’s Most Magical Number, many historians believe that Phidias successfully applied the golden ratio in his writings. .
Phidias.
That’s why mathematician Mark Barr decided to honor Phidias by naming the symbol Φ Phi. Therefore, Phi is not a discovery discovered by Fibonacci (it was also studied and defined by Euclid) and the name Phi has no “Italian flavor” at all (spaghetti taste? ).
Even so, we still need to learn more about Fibonacci’s discovery to better understand the wonderful balancing potential of Phi and the numbers that arise from it. The Fibonacci success and the golden ratio figure are two sides of the same coin.
The Fibonacci sequence was discovered by the “mathematician from Pisa” – the sequence 0; 1; 1; 2; 3; 5; 8; 13 … – in the field of arithmetic, the study of numbers and the basic transformations that can be done with these numbers The golden ratio, represented by the name Phi (symbolized by Φ, φ) comes from a success in arithmetic, representing the relationship system of two elements on a line segment True, Phi has a geometric structure shown as shown below:
We use algebra to find the numerical value of Phi (Φ), we use the simple formula Φ=a/b. We apply this formula to the geometric representation of the image above, when taking the total length of the line segment (a + b) divided by the longer segment (a), we also get the same result when taking the longer segment ( a) divide by the shorter segment (b). To sum up, we have Phi (Φ) = (a+b)/a = a/b .
The result of this equality is 1.6180339887…, the same value as the golden ratio defined by the mathematician Euclid, as described by Mario Livio as “an infinite and non-repeating number”.
Curiously, this number is very similar to the result when dividing any consecutive number in the Fibonacci sequence by each other (e.g. 5/3=1,666; 13/8=1,625). Combining these two factors, we have succeeded in using geometry to represent an arithmetic category.
This is what makes this article interesting, it doesn’t take a mathematician to understand and see the beauty of algebra. Moreover, we understand more about the fundamental arithmetical property of the discovery of the great mathematician from Pisa: the famous Fibonnaci spiral.
The properties of the number Phi amaze us, and its discovery in the form of the golden ratio has given us a way to analyze forms, objects, geometrical representations and even are movements in nature that still take place in this world. It brings up a saying that has been mentioned elsewhere in this article: the golden ratio or the divine proportion .
In the images above, we see the Fibonacci spiral, the rectangle with the golden ratio but in addition, it can also be used to identify the golden ratio triangle or the pentagon. But they all have one thing in common: they all have the “golden element” in them.
The pentagon with the golden ratio.
These golden ratio numbers are self-created, is the environment around us so “golden” or so “divine”? Architectural works with the golden ratio are made by humans, does Mother Nature apply that formula in construction?
The answer is yes. We can see the golden ratio in the Pyramids of Giza 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 (2nd time), in the music Dialogue du vent et la mer by composer Claude Debussy – the Fibonacci sequence appears 50 musical bars, which can be divided into lengths of 21, 8, 8, 5, and 13 bars.
The Golden Ratio of La Gioconda.
The golden ratio of the galaxy.
The appearance of the series of numbers, of this magical golden ratio is everywhere. So is it enough to call it the most interesting number in the world? Based on this number, can we change reality to do the impossible, create a no-math-free world? But without a doubt, these facts show us that the math that makes us feel like seemingly unrelated things have something in common: a sequence of numbers holding them back.