Calculation of Golden Ratio - The Incredible Truth
GOLDEN RATIO CALCULATION
Mathematics is the mother of science and all languages.
Mathematics was not invented rather it was discovered by human. Mathematics is
the best language to communicate as we can transform everything, every action
into a mathematical form, and Golden ratio is one of the most genius examples
of them.
The Golden Ratio is
one of the most incredible discoveries of mathematics. It is a geometrical code
of the Universe which was encoded by some genius mathematician and artists.
Explanation

This rectangle is called golden rectangle and the relationship between
these lengths (A,B) is,
(A+B)/A = A/B = phi = φ
Phi (φ) represents the golden ratio.
Calculation
Let’s take the equation
(A+B)/A = A/B = φ ………………………….(i)
Now, taking only the left hand side,
(A+B)/A = A/A + B/A = 1 + B/A = 1 + 1/φ [ as, φ = A/B ]
Therefore,
1 + 1/φ = φ [
from equation (i) ]
(φ + 1)/φ = φ
φ2 – φ – 1 = 0
Now, using quadratic equation, two roots of φ are obtained
And,
φ = +1.61803…
= -0.61803…
But, Golden Ratio is the
ratio between two positive numbers. Since, the ratio of two positive numbers is
also necessarily a positive number, so only the positive root of phi is taken.
φ = 1.61803…
Conclusion
This ratio is very interesting to understand and important in mathematics. The Golden ratio helps us to the nature of the universe. In this universe, from the huge Galaxy to the tiniest material DNA, all follow the golden ratio. Every living organ, animals nature, plants nature, human body everything follow the golden ratio. Golden ratio is hidden in between the physics, chemistry, solar system also. All we just need to understand and find.
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