PHI... A ratio found everywhere

PHI Φ, the Golden Ratio (or Golden Number), a ratio that could be found everywhere. This is also known as Divine Proportion. I didn't know this until i read the book The Da Vinci Code. I got mesmerized when i was reading about it. Got to know many interesting stuff.

Well, the value of PHI, Φ is : 1·61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 or (√5 + 1)/2, which a rational number and the value of this has been calculated till 20000 places but in general its value is taken as 1.618.

Easiest number to get the square.

Square of phi is just adding 1 to it. Φ² = Φ + 1. Isn't it easy? and Isn't it amazing?

Fibonacci Series and Golden Ratio

There is a very interesting relation between PHI and Fibonacci Series. i.e. The ratio of successive fibonacci numbers get closer and closer to the number Φ. Or you can say the ratio of successive fibonacci number oscillate around the number 1.618.... or Φ.

1,1,2,3,5,8,13,21

1/1 = 1 < Φ 2/1 = 2 > Φ
3/2 = 1.5 < Φ 5/3 = 1.666666666666666666667 > Φ
8/5 = 1.6 < Φ 13/8 = 1.625 > Φ
21/13 = 1.615 and so on < Φ Isn't it amazing?? Wow!!! i felt it quite surprising. Golden Section:

The Golden Section is also known as the Golden Mean, Golden Ratio and Divine Proportion. It is a ratio or proportion defined by the number Phi ( = 1.618033988749895... )

It can be derived with a number of geometric constructions, each of which divides a line segment at the unique point where:

the ratio of the whole line (A) to the large segment (B)

is the same as

the ratio of the large segment (B) to the small segment (C).

In other words, A is to B as B is to C.

This occurs only where A is 1.618 ... times B and B is 1.618 ... times C.

Divide the line again and again in the same way:

This is known as "Golden Ruler"

This appears in the proportions of many life forms.

This ratio has been used by mankind for centuries

It was used in the design of Notre Dame in Paris and continues today in many examples of art, architecture and design.

The Renaissance artists knew it as the Divine Proportion and used it for beauty and balance in the design of art

It also appears in the physical proportions of the human body, movements in the stock market and many other aspects of life and the universe.

The Divine Proportion in the Body

The white line is the body's height.

The blue line, a golden section of the white line, defines the distance from the head to the finger tips

The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows.

The green line, a golden section of the yellow line, defines the distance from the head to the pectorals and inside top of the arms, the width of the shoulders, the length of the forearm and the shin bone.

The magenta line, a golden section of the green line, defines the distance from the head to the base of the skull and the width of the abdomen. The sectioned portions of the magenta line determine the position of the nose and the hairline.

Although not shown, the golden section of the magenta line (also the short section of the green line) defines the width of the head and half the width of the chest and the hips.

There are many interesting relation between PHI and our nature. An endless number of relations. For greater details check out: http://goldennumber.net/