I have always had a fascination for numbers and the theories related to them. But, I had not put in much effort to go through the various theories on numbers. But, very recently, I came across a theory called the "Phi Theory" and was really intrigued by it. The Phi theory has close relation to the renowned Fibonacci series. The golden ratio (also called Phi) forms the solid base for the Phi theory.What is the golden ratio (Phi) ?
The Golden Ratio (or Golden number) is named after a Greek letter,Phi. The numerical value of 1·6180339887... is referred to as the golden ratio.
A clear-cut definition of Phi.
As we all know, there are just two numbers that remain the same when they are squared namely 0 and 1. Other numbers get bigger and some get smaller when we square them.
But, what makes Phi special is that, we can obtain the square of Phi by simply adding the value 1 to Phi.
In simple terms,
Phi2 = Phi + 1
It is bewildering that there are just two numbers that satisfy this property ( Square of the number = Number + 1). One such number is the Phi, while the other is called as "phi" and holds the value of 0.6180339887... This is exactly the decimal portion of Phi. Phi and phi are closely related to each other in the sense that, they are the solution to the above cited equation (Phi2 = Phi + 1).
It is also worth a note that Phi = 1/phi = phi + 1. Thereby, Phi and phi have a deep rooted relationship.
Significance of the Golden Ratio.
It is believed that Golden Ratio has a deep connection to the beauty of nature and things. It is being held that, any object whose proportions equal the golden ratio, tend to be pleasing to the eye. There are several citations for this conjecture.
In addition, several splendid pieces of human creation as well as the enticingly beautiful aspects of nature and living forms are found to exhibit the "Golden Ratio" in their proportions.
Phi Theory in Nature and Human Structures.
Nature and Human structures strikingly seem to represent the Golden Ratio. A plant named "sneezewort": Achillea ptarmica, exhibits growth ratio that equals the Golden Ratio. Also the number of petals on many flowers is found to be a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals. The most intriguing one is the Seed arrangement in a Sunflower. It is found that the ratio of the Number of seeds arranged in the Anti Clockwise pattern to the number of seeds arranged in an Clockwise pattern equals the Golden Ratio.
Even the alluring Pyramids are belived to typify the Phi. The ratio of the length of a face of the Great Pyramid (from centre of the bottom of a face to the apex of the pyramid) to the distance from the same point to the exact centre of the pyramid's base square is about 1·6. It is a matter of debate whether this was "intended" to be the golden section number or not. The Phi is believd to be exhibited in shapes of galaxies, Human DNA, Human face and several other aspects.
So to conclude, Phi theory is one of the most enigmatic and intriguing theories in Mathematics. It has colligation to several theories in Physics too. For more information, one can Click Here and get to know in depth about the Phi Theory.
It is also worth a note that Phi = 1/phi = phi + 1. Thereby, Phi and phi have a deep rooted relationship.
Significance of the Golden Ratio.
It is believed that Golden Ratio has a deep connection to the beauty of nature and things. It is being held that, any object whose proportions equal the golden ratio, tend to be pleasing to the eye. There are several citations for this conjecture.
In addition, several splendid pieces of human creation as well as the enticingly beautiful aspects of nature and living forms are found to exhibit the "Golden Ratio" in their proportions.
Phi Theory in Nature and Human Structures.
Nature and Human structures strikingly seem to represent the Golden Ratio. A plant named "sneezewort": Achillea ptarmica, exhibits growth ratio that equals the Golden Ratio. Also the number of petals on many flowers is found to be a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals. The most intriguing one is the Seed arrangement in a Sunflower. It is found that the ratio of the Number of seeds arranged in the Anti Clockwise pattern to the number of seeds arranged in an Clockwise pattern equals the Golden Ratio.
Even the alluring Pyramids are belived to typify the Phi. The ratio of the length of a face of the Great Pyramid (from centre of the bottom of a face to the apex of the pyramid) to the distance from the same point to the exact centre of the pyramid's base square is about 1·6. It is a matter of debate whether this was "intended" to be the golden section number or not. The Phi is believd to be exhibited in shapes of galaxies, Human DNA, Human face and several other aspects.
So to conclude, Phi theory is one of the most enigmatic and intriguing theories in Mathematics. It has colligation to several theories in Physics too. For more information, one can Click Here and get to know in depth about the Phi Theory.
1 comments:
Nice synopsis
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