Where can we find the golden ratio on earth and what can we achieve from finding it?
It is well known that the golden ratio and Fibonacci numbers are ubiquitous in our universe, and Earth as a physical object is the main subject in geology as a science. So Where can we find the golden ratio on earth and what can we achieve from finding it?
The golden ratio point may play a role of origin similar as Euclidean & Riemannian geometry. Though, Issam Kaddoura provided very useful links for answering to your query, I would also Re-mention the https://www.goldennumber.net/golden-ratio-of-earth/ as the best.
Historians of mathematics and art, even today, have been unable to determine with certainty when golden ratio appeared for the first time in some of the old civilizations, but they all agree that golden ratio, purposely or not, was applied in ancient Egypt in the construction of the Cheops Pyramid in Giza (one of the seven wonders of the old world that still exists today): the ratio of the height of the facet to half the length of the base edge.
Next, the golden ratio that was notably used in ancient and Hindu architecture, Gothic architecture, Renaissance, and later in classicism, usually for the design of faces or ground plans of temples, mausoleums, churches and cathedrals: Parthenon at Athenian Acropolis (432 BC), Taj Mahal in Agra (1653), cathedrals in Anagni (1104), Florence (1436), Milan (late 14th century), Paris (1345), Reims (1275).
Taj Mahal Mausoleum ina Agra: the outer frames of the main building as well as the frame of the main gate are golden rectangles.
The golden ratio is evident in the formation of waterways, such as rivers and tributaries. as water typically follows the path of least resistance, and their courses are ever changing, perhaps this lends credence to the golden ratio being ever present in the geologic formations that comprise the Earth's crust. Close consideration should be given to the geologic formations in this regard.
Further evidence exists in the typical tracks of tropical storms, such as hurricanes and typhoons. The concentric circles that form throughout the rotational lifespan of these storms is evidenced in the heliocentric paths these storms follow during migration. Weather patterns are often consistent with following the golden ratio as they move across the planet.
These are just a few thoughts off of the top of my head, as I am no expert on the matter, but in working with soils, I often find the correlation proven more than disproved.
I have speculated this issue for my own sake for more than 1 year. In short, I came to this conclusion that everything in the real-world is structured based on a complicated mathematic which is beyond our conventional math science since Euclidean geometry simplifies all creatures to the simplest imaginable geometrical form which could not be found in nature. Let me put it in this way, have you ever seen a straight line or perfect circle in nature? In other words, the mathematic we are using is not completely adaptable with what we are seeing out there. By and large, although we have reached complex structures with high computational orders for capturing complex structures (Fourier, wavelet,...), our mathematic is yet poor to capture the shape of a tree perfectly.
Now let me tell you about fractals geometry that presented abundantly in nature such as flowers, shells, etc.. This is where our math could be applicable if we consider portions, and golden ration is one of there portions. Indeed, using ratios we could bridge between our invented math with real-world phenomena. In summary, this issue is very complex and we cannot express anything for sure.
[Let me put it in this way, have you ever seen a straight line or perfect circle in nature? In other words, the mathematic we are using is not completely adaptable with what we are seeing out there.]
What do you think about the orbits of planets, stars, and particles in the atom? Are they part of nature or not? Look at your eye, is it a part of nature or not?
Fractals, as well as Fibonacci numbers, exist everywhere in nature.
So you can observe the structure of almost every living thing is strongly based on the golden ratio.
Just Google :
Golden ration in nature
Golden ration in the human body
Golden ration in the universe
in physics, chemistry, etc., you will see thousands of papers and articles about the topic. Besides, you believe the shortage of mathematics to find models for phenomena in nature!! So, my advice to you is to read something about chaos theory and dynamical systems.
I am not following your reference [" What do you think about the orbits of planets, stars, and particles in the atom? Are they part of nature or not? Look at your eye, is it a part of nature or not? " ]
You are of course aware that all of these objects, from the orbits of planets and atoms to the human eye are in fact not perfect circles, but oblong ellipses, or ellipsoidal planes, are you not? The eye itself is oblong. This tends to lend credence to @ Hamed Majidian statement on [ have you ever seen a straight line or perfect circle in nature? ]
The objects that you reference are affected by gravity, which is the transcendent force across our universe. This would tend to imply that gravitational forces would prevent any object in motion, such as atoms, which make up everything, from following a simple circular trajectory. This is the foundation of relativity.
I would very much be interested in following your logic and thought process on this.
If you accept the existence of ellipse, then we are done.
The circle is a particular case of the ellipse that has more amazing properties than the circle, the same for Cassini's ovals.
Roughly speaking, the trace of a free-falling object may be considered as a straight line, somebody may think the light ray as straight-line propagation!!
Is it the case? To judge and describe objects, man creates mathematical models as Euclidean geometry by the geometric and algebraic postulates.
The main point, what is the definition of nature? All figures, regular or irregular shapes are reflections of our consciousness to our surroundings; different creatures with different senses may feel and see the same object in different ways. So, axiomatics is the solution.
Different axioms create different geometries. Many scientists agree that our universe is not Euclidean so that you can expect anything. For example, the sum of angles inside a triangle may be equal, greater, or less than 180 degrees; this will be decided by the choice of the axioms of the mathematical model.
I think you are familiar with Euclidean geometry, where the sum is 180 degrees.
By the way, what a straight line is? Nobody can guarantee the straightness of the (straight line ) as well as the continuation of its points!! It is a profound problem. Going back to nature, we are trying to observe and study our surrounding; the main problem is to adopt the suitable geometry to explore the real universe, Einstein used Minkowsky space-time to show his GRT and SRT. Many physicists consider our universe as flat, others said it is an elliptic one, and some of them tell that it is the hyperbolic universe! We are still at the starting point when we answer one question, hundred of more questions be raised!
Our humble knowledge allow us to follow and observe the Fibonacci numbers
where its ratio Lim (Fn+1/ Fn ) goes to (1+sqrt(5))/2 = 1.618..the golden ratio,
as n goes to infinity. The literature is full of articles that tackle the existence of such a ratio. Our observations are full of geometrical phenomena such as fractals, vortices, strange attractors, etc. We can see that our universe is created in an optimum way that we are trying to understand.
Jubilado del Mexican Institute of Social Security, Universidad Nacional Autónoma de México
Dear Yosef Mousavi
Agree with many of the previous answers. It is based on the Fibronacci number or series. It is the infinite sequence of natural numbers:
The golden ratio can be found in nature and is the shape of complex structures such as the petals of a flower (sunflower) or the leaves on a stem, or the branches of a tree, etc; They are organized in the smallest possible space while maintaining the most efficient architecture from a functional point of view.
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MerriamD. F. (Ed.) 1978. Recent Advances in Geomathematics: An International Symposium. xii + 233 pp. Contains 13 articles presented at sessions sponsored by the International Association for Mathematical Geology at the 25th International Geological Congress, Sydney, Australia 1976. Computers and Geology, volume 2. Oxford: Pergamon Press. Price $30...