Digging Deeper into the Golden Ratio

Mona Lisa Golden Ratio
Leonardo Da Vinci seems to have made extensive use of the golden ratio in his creation, Mona Lisa

The golden ratio, or the divine section, A+B:(A+B)-B or (A+B)/A, represented by phi and it’s ratio to one. Occurs when the ratio of two numbers equal their sum. As is, as to. Everything follows the pattern that created it, in mathematics, and in nature. The true golden ratio is a ratio applicable for determining the past, present, and future states of any pattern, even outside of numbers.

It is believed that this ratio is everywhere in nature. Over 2300 years old, perhaps this is the reason we find the golden rectangle, a rectangle whose shorter side is as to the golden ratio to the longer side, aesthetically pleasing? Perhaps aesthetic pleasure occurs when the brain witnesses the pattern it is most familiar with, when nature views it’s reflection.

A synopsis of the Golden Ratio

Its the gold standard of ratios! A golden ratio, also known as a golden section, golden mean, and divine proportion is related to fibonacci’s sequence of numbers.

Mathematicians as old as Euclid studied it’s appearance in the regular pentagon and the golden rectangle. in 300BC. In a pentagon, the area is one half the perimeter multiplied by the apothem. Here the golden ratio can be illustrated through the five fold symmetry of the pentagon, the apothem represents B and any side of the pentagon is A, as to the golden ratio.


The golden ratio was also studied by Greek mathematician Pythagoras. The Pythagorean theorem, a² + b² = c², as to the golden ratio, a as to c² and c, as a² + b². The Pythagorean theorem arises from the value of phi, the only number that’s square is one more than itself. Illustrated by 1+√Φ=Φ, a²+b²=c², 1+2=3.

Optical Tricks of the Parthenon

However it goes back even further as far as the history of civilized man. It is known that dimensions of pi and phi were used in the construction of the great pyramids of Giza.

golden ratio in architectureSupposedly the great pyramid’s base is 230.4 meters, as to it’s height, 146.5 meters, are at a golden ratio, forming golden triangles at the pyramid’s sides. It’s surface ratio is also analogous to that of the golden ratio. Geometrically the great pyramid can also represent pi, the difference of a circles radius to it’s circumference.

These things may not seem very significant, but one could reach an understanding of these rates and ratios past the numbers once it is known that the great pyramids existed before civilized man even had recorded documents of the values or even the numbers themselves for pi, and phi, yet they appear almost perfectly in these huge megalithic archaeological structures.

Does this suggest that the meaning of these rates and ratios is beyond the perfect math we use to understand and represent it?

Dr. Daniel Lordick – Architectural Fractals


Structures of stochastic self-similarities can sometimes be found in architecture. Frequently mentioned examples are Gothic cathedrals, the Eiffel Tower, and a class of Indian temples.

If you understand the truth of the golden ratio behind the mathematics, as the application that is self applicable to everything, even determining the past, present, and future states of any pattern. By plotting the points of a pattern, a system emerges, this system could be used to determine the value of it’s future iterations.

For example, if one is valued by two halves of 0.5, then two equals fourths of 0.5, and three equals sixths of 0.5. In time, and quantum wave physics, with the partial momentum of any object you can determine total velocity. The ratio illustrates how our perception of reality is determined by a higher awareness of what reality is. Everything becomes as to what it has become.


Golden Section in Art and Architecture

Golden Ratio


The Golden Number

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