Question

An important proportion that the ancient Greeks used was the a0.

Answer 1

Golden Ratio?

a/b=b/(a+b)

a^2+ab=b^2

b^2-ab-a^2=0

b=(a(+-)(a^2+4a^2)^(1/2))/2

b=(a+a(5)^(1/2))/2

b≈1.618

Answer 2

Explanation:

Golden ratio is a special number found by dividing a line into two parts so that longer part is divided by the smaller one is equal to whole length divided by longer one.

a/b = (a + b)/a

a² = b(a + b)

a² = ab + b²

a² - ab - b² = 0

Now from the quadratic equation

a = [+b ± √(b² + 4b²)]/2

a = b×[1 ± √(5]/2

a/b = (1 + 2.236)/2 = 3.236/2 = 1.6180

This is the golden ratio is 1.6180 denoted by Phi.