Golden Ratio Known as the Divine Proportion - Essay Example

Leonardo Fibonacci (1170-1250) had also shown that the ratio of neighboring Fibonacci Numbers tends to Golden Ratio. (Knott)A simple definition of the Golden Section (Φ) is that the square of it is equal to itself plus one. The value of Φ is or 1·6180339887 (approximately). Geometrically the definition of Golden Section (Φ) can be given by the below method.

(Weisstein 742-744)Let the ratio Φ ≡ AB/BC. Therefore, the numerator and denominator can be taken as AB = Φ and BC = 1. Now defining the position of B as Or Solve the above equation using the Quadratic equation. The Ratio of neighboring Fibonacci Numbers tends to Golden Ratio. The Fibonacci Numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233. And their successive ratios (ignoring 0) are 2/1= 2, 3/2=1.5, 5/3=1.666., 8/5=1.6, 13/8=1.625, and so on. (Freitag)There are many things interesting about Golden Ratio (Φ).

It is the only number that when one is subtracted from it results in the reciprocal of the number (). Golden Section (Φ) is the most irrational number because it has Continued Fraction representation as Φ = [1, 1, 1, 1, 1, 1…]. Golden Rectangle (above figure) is a geometrical figure that is commonly associated with Golden Ratio. The sides of the Golden Rectangle are in proportion to the Golden Ratio and it is the most pleasing rectangle to the eye. It is said that any geometrical shape that has the Golden Ratio in it is the most pleasing to look. Golden Ration has connections with Continued Fractions and the Euclidean Algorithm for computing the Greatest Common Divisor of two Integers.