(Animation from GIPHY.com)

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Is it possible that a ratio could exist, which is geometrically applicable to countless formations across the natural world? An almost blueprint-like commonality in design, spanning across the perceivable universe?

The short answer to that question, is yes, sort of.

Physical dimensions allegedly applicable to this “golden ratio” range from the shell of a snail, to the shell of a nautilus (most logarithmic spirals are linked to the golden ratio, regardless of accuracy), to the tail of a seahorse, to the formation of a rams horn. The proportions of human limbs, the formation of cyclones and even the celestial alignments of galaxies millions of light years away. (There is no shortage of alleged examples of the golden ratio.)

Some have claimed that this reoccurring ratio found throughout the universe is a mathematical sign of the divine. That the mere existence of such a reoccurring pattern behind what many would assume to be utterly random, defies their preconceptions of what is logical. That the very thought that the same 1:1.6 ratio that is found from the tip of a humans head, to their belly button, then down to their feet could be found in the circular dispersion of seeds on the face of a sunflower: to many, that seems absolutely irrational.

Irrationality, however, may be precisely why this occurs.

**Irrational Numbers: ***(of a number, quantity, or expression) not expressible as a ratio of two integers, and having an infinite and non-recurring expansion when expressed as a decimal. Examples of irrational numbers are the number π and the square root of 2. *—Oxford Dictionary

Imagine you have a spinning wheel, with a flat white circular front. You mark a dot in the center of the wheel. You could mark this wheel to show segments displaying the degrees of revolution. As seen below:

If you were to start at the point marked 90° and rotate the wheel exactly 90° clockwise, the part of the wheel marked 180° would now be centered at the top. Another 90°, the point marked 270°, and once more, finally, the point marked 360°. Doing this over and over again, regardless of how many times you do it, you will always land on those 4 specific points marked on the circle.

Again, if you instead turned the wheel 1°, starting at 90°, you would first land on 91°, 92°, 93° and so on. In all, making 360 1° turns until arriving once more at the starting point marked 90°.

But what would happen if instead of moving 90° each rotation, you moved φ, which could be expressed as 360°/1.618… which is equal to = ~**222.5°**

Unlike the original 90° rotations, always arriving at the same 4 specific points, over and over again, with these ~**222.5°** rotations, we notice something interesting occur. These much wider gaps, are far less likely to overlap, almost resistant to the notion. Time after time, with each rotation, off-centering from the last. Due to the nature of the irrational number, converted into ~**222.5°**

Even the leaves of a plant apply this formula to the directions in which they grow, because if they can systematically stagger their leaves **not **to overlap, they can absorb the maximum amount of sunlight.

The problem for many of us, when we find this Golden Ratio in all sorts of places, we immediately assume this formula, this ratio was taken into consideration at the formation/design of whatever we’re looking at in the natural world. When in actuality, what we are looking at, is as close as we can currently perceive, to what could be regarded as perfect mathematical irrationality.

The Golden Ratio appears on the face of a sunflower in the arrangement of its seeds, because evolution discovered the optimum means to distribute seeds, which happens to be perfect mathematical irrationality. The leaves of a plant grow in the formation of the Golden Ratio, because evolutionary, those which stumbled upon (through genetic deviations) the formation received the most sunlight and were the most successful in reproducing themselves. The process could only refine itself, further and further with time and natural selection.

It is generally regarded (with varying accuracy and significance) that the Golden Ratio appears in physics, chemistry, biology and even (controversially) the topology of space-time. Are we simply conflating perceivable irrationality, of unrelated data due to broad similarities of dispersal/proportional arrangements? (due to the Heisenberg uncertainty principle) Or is the Golden Ratio far more intrinsically linked with the nature of our universe than we currently understand?