# Golden Ratio

Golden ratio, also known as the golden section or divine proportion, in mathematics, the irrational number (1 +√5)/2, often denoted by the Greek letter "phi" ϕ or τ, which is approximately equal to 1.618

The Idea Behind It

The golden ratio divides a line into two parts so that: the long part divided by the short part is also equal to the whole length divided by the long part.

A more accurate way to describe it would be, to call it a ratio of line segments when a line is divided into two parts (a and b), such that the ratio of ‘a’ to ‘b’ is the same as the ratio of (a+b) to ‘a’

## Golden Ratio in Real World

Flower
In the interior of a flower the ratio of every level’s granule to the next level’s granule is = 1.6180…
Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece, but it is not really known if it was designed that way.

DNA
A DNA molecule is 34Å in length and 21Å in width. The ratio is approximately equal to the golden ratio.

Human body:
Yes, phi is present in human body. Such as,
Total length of human body : Lower part of the body from navel = 1.6180…
Shoulder to knee : Knee to toe = 1.6180…
Human biceps : Hand = 1.6180…

In a Human body we can find more than 300 such types of Golden ratio.

## The Actual Value

The Golden Ratio is equal to:
1.61803398874989484820... (etc.)
The digits just keep on going, with no pattern.

## Formula

We saw above that the Golden Ratio has this property:
ab = a + ba
We can split the right-hand fraction like this:
ab = aa + ba
ab is the Golden Ratio φ, aa=1 and ba=1φ, which gets us:
φ = 1 + 1φ
So the Golden Ratio can be defined in terms of itself!
Let us test it using just a few digits of accuracy:
φ =1 + 11.618=1 + 0.61805...=1.61805...
With more digits we would be more accurate.