the Golden Ratio--I

u myt find this interesting...if u gt a litl interest in math

Which is the world’s , most interesting number? Put a poll…ther some might say pi, e, ‘i’…gosh there r so many numbers to choose from.. there might be some who wil stand for ‘phi’.

Well wats so interesting about this number…lets explore it!

One of the easiest way to define phi is

‘phi’= (1+sqrt 5)/2

This gives phi= 1.6180

This is jus an approximation guys…use sci calc n the length of the number increases linearly with the accuracy of ur calc!

Well the phrase “golden ratio” comes from the golden rectangle

See the figure adjoining

The golden rectangle has a unique property…if we remove a square from it, what remains is a smaller rectangle with the same shape as the original!

Equating the aspect ratios gives

1/φ = (φ-1)/1

Observe the equation…it states that the reciprocal φ can be calculated by subtracting from it. Think of another number that has the same property!

Φ and its reciprocal are the only two numbers whose reciprocal can be calculated by subtracting ‘1’ from the other.

Putting it in the form of an equation we get

φ² – φ – 1 =0;