## Sunday, 20 July 2008

### Golden Ratio - an interesting maths invention

There are many inventions and discoveries by mathematician of the past. One of them is the Golden Ratio.

Golden ratio (or Golden Section, Golden Mean) is a ratio defined by a special irrational number "phi".

This number "phi" equals to 1.618033988749......... and goes endlessly. This "phi" is actually a solution to a quadratic equation y2 -y -1 = 0.

The fantastic Golden Ratio can be explained using division of a straight line shown below.

A 1

------------------------------------------------

By dividing the straight line above into two sections, namely, A part and 1 part, the ratio of A / (A + 1) = 1 / A , we obtain the Golden Ratio.

The solution to this (that is solving for A) produces the irrational number "Phi".

The solution or the dividing point on the line cannot be anywhere. It has to be a point satisfying the relation A + 1 = (1.618.....) multiply A.

In real life, we can see the ratio and "Phi" applied in many areas:

1) In the Egyptian Pyramids

2) In Feng Shui studies

3) In the Arts and Architecture fields

4) In Music composing

5) In Stock Market analysis

6) In the medical field

7) In human anatomy

etc.

With the wide applications it involves, no wonder, it is called the GOLDEN Ratio!