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Golden Ratio, Phi, 1.618, and Fibonacci in Math, Nature, Art, Design, Beauty and the Face. One source with over 100 articles and latest findings.
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Hey guys just ran across your site here. I was interested in Phi for two years now and been interested in the subject ever since. I read many sites and saw many demo videos on Youtube about it. It really does make a lot of sense when you see the evidence of this golden number in every part of the natural sciences. I’m surprised they never taught this in school, at least I didn’t hear about it. It definitely is the proof that there is a superior designer or Creator of our universe and everything that lives in it and that is born from it. This golden number is existent in almost any and every form that is natural in the universe. The code and the basic blue print that makes everything else in our universe. I like to use this in my art techniques when composing ideas. A golden mean gauge is a great tool for designing. Another tool I haven’t seen yet in existence is a “golden angle compass” (137.5…degress). I experimented with this number 137.5 and found that when drawing angle points based on 137.5 degress it never lands on the same spots from before. New spots are made to infinity. Hope I’m not reinventing the wheel here. Thought I share some ideas I had if not known already. —Edward.
Yes, Phi could be taught in art, design, math, geometry, biology and other courses. For those reading this post who aren’t familiar with a “golden angle,” take 360 degrees and divide it by 1.618 to get two sections of the circle in golden ratio proportions, one at 222.5 degrees and the other at 137.5 degrees. It’s found in the arrangement of stems in plants to optimize access to sunlight and room for growth.
Dear Gary ,
Yes very interesting
Similarly if we take the inverse of 2.618033989 = 0.381966011
and multiply it by 360 we get 137.507764.Subtracting this from 360 we get 222.492236.
By the way in Greece[ 38 PARALLEL approx. Athens ] we have the longest day [ 21 Jun SUN RISE 05:03 – Sun Set 19:51,Dif=14 H:48 First= 14.8H, RATIO 24H/14.8H=1.62…].
Also the 38 deg Parallel approximates with the 90-38= 52 deg G.PYRAMID SLOPE.
Regards from Athens,
Panagiotis Stefanides
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http://www.stefanides.gr/
Also the 38 deg Parallel approximates with the 90-38= 52 deg G.PYRAMID SLOPE.
Regards from Athens
I have been working with a structure that was designed to work with the sun and built to Phi Pi. At cross quarters the shadow from the dial post is .618 at 12:00 ,1.618 at 5:00 . All of the windows doors and floor plan interact accordingly throughout the year.
The roof pitch is 52 deg and a lower surrounding roof is 38. The design of the building is called a Greek cross. The Architect Wren was located in the co latitude of approx 52 England.
The three sights I have observed with similar phenomenon correspond to Adelphi, Athens and Delos in America
When an analema is made by marking each day at the same time ,the figure eight crosses at PHI
when did fibonacci discover Phi?
To the best of current knowledge, Fibonacci discovered the sequence named after him (0, 1, 1, 2, 3, 5 … ) but never realized or discovered that the ratio of each term to the one before it converges on Phi.
Kepler discoverd Fibonacci sequence by himself years after Leonardo Fibonacci. Kepler also discoverd the ratio of each term to the one before – Phi.
“”It definitely is the proof that there is a superior designer or Creator of our universe and everything that lives in it and that is born from it.””
There’s nothing creationist about it. Nature doesn’t do arithmetic – it’s a human abstract concept. It just takes the last quantity it made and adds that to the one before that, hence 0,1,1,2,3,5,8,13,21,34,55 ad infinitum. As the quantities grow, the ratio of latest to previous settles to 1.61803. No gods involved.
It’s not that simple. There are certainly instances of phi/Fibonacci appearing as a result of efficiency in a growth pattern but then there are many other instances, in the human form for example, where its appearance has no obvious or functional reason other than for sheer beauty and our ability to perceive it. If we’re truly honest we have to admit that we don’t have answers as to life’s origins. If we genuinely want to grow in our understandings of the truth we must seek with an open mind on both sides of this issue and investigate all possibilities. As Einstein said, “Science without religion is lame, religion without science is blind.” There are no proofs here, only evidences whose interpretation is very dependent upon biases, experiences and belief systems of the individual. Those who have had personal life experiences of God and the spiritual side of human existence have little difficulty seeing a greater design and purpose in the world around them. Those who have not will find it more in line with their experiences to see the world through a naturalistic filter or viewpoint.
I could not have put it better myself. Nature does do mathematics simply because it is incapable of working out any other way. Right back to Higg’s Boson. Humans merely see the patterns and fit them into their own perspectives.
I just wish that ‘ religion’ would use Occam’s Razor to see that the Universe and Nature could create itself as part of a continuum far beyond our measurement of time and space. Not that God does not have a place but whatever ‘it’ is a direct consequence of Nature and our own evolution rather than the other way round.
Your application of Occam’s Razor reflects an atheistic or non-theistic world view, as does your statement that God must be a consequence of nature rather than the cause of it. Occam’s Razor is appropriate for matters of scientific evidence and testing but not for metaphysical topics such as the origin of life and existence of God. The Razor says that given two competing theories, the simpler explanation is to be preferred, but the definition of “simpler” is subject to interpretation. The myriad of chance events with astronomically low probabilities required to create a universe and intelligent life within it can hardly be defined as “simple.”
This statement – ‘Not that God does not have a place but whatever ‘it’ is a direct consequence of Nature and our own evolution rather than the other way round’ – by Alan is truly, utterly absurd, and proves, if proof ever were needed, that there are many today who simply have no idea what the concept of God actually entails.
How, Alan, can God (or ‘god’) be a ‘consequence of Nature’? In making this claim you are elevating ‘Nature’ to a position higher than the creator of that nature, for, among other things, in order for ‘God’ to be such it would have to transcend any and all of the limitations that ‘nature’ will place upon all that exists within it (ex. temporal limitations).
You clearly have not given this issue much, if any, thought.
I always like to think of what came first, mind or matter? I believe I am correct when I say mind, as matter cannot create mind, hence mind over matter, although please correct me if I am wrong.
The Bible states “In the beginning was the Word, and the Word was with God, and the Word was God”; I take this as being that in the beginning there was a sound and this sound was the creator of everything, and then you look at Cymatics the study of how sound can create and affect images, patterns, tidal movements and objects; and how all things are made from Atoms which are almost entirely empty yet due to a vibration frequency (sound) can appear to be solid, soft, hard, smooth and rough, in fact they are everything around you now; so as with the Fibonacci sequence and the golden ratio, there are patterns; the Golden Pattern for me is the link between Mind (Conscious and subconscious) and Matter, including dark matter and applying the Golden ratio and Fibonacci sequence to encompass both mind and matter.
Aug 6 1945 Tinian-dad was there-now in radiology we use radiation for dx and healing–Along the way I encountered the spiral cochlea – used the Nautilus to help us recognize anatomy
So many associations it has confirmed a good orderly direction as a design for us-our planet
and probably the universe-For this preachers kid that has been infinitely reassuring 🙂
‘There’s nothing creationist about it. Nature doesn’t do arithmetic…’
Well, apparently here is evidence that nature, or that which underlies and is responsible for there being ‘nature’ in the first place (God?), does indeed ‘do arithmetic’. Your response indicates to me that you really have not considered the implications of the numerous discoveries found within nature of this ratio, for it is quite obvious to those of us who have that this is much more than just a ‘human abstract concept’ – it is intrinsic to nature, and is not just another example of a pattern that appears as a result of attempts made by us to project order onto randomness, as so often happens (ex. the constellations). If this fact doesn’t convince you that there is an underlying intelligent purpose to the very real order we see around us, then I don’t know if there is anything that ever would. Oh well, your loss.
Peter, Everything works together for a greater purpose, more than you can even begin to fathom. We are limited by our sight, hearing, tasting, feeling, and smelling. Look beyond and open your mind, nature does do arithmetic!
Yes I know. That is what I pointed out in my response to RobinB. The first sentence is a quote from him (or her?), hence the inverted commas.
… It definitely is the proof …??? omg Edward!
Pascal said it best – There is enough light to see God’s hand and enough darkness to hide it. It is the nature of faith in God that it is not falsifiable. The existence of God is compatible with any state of affairs. Now we see through glass darkly but then we shall see face to face.
Nature / particles are self-organizing but are sustained by the power of God. We are part of God’s dream. We did not make ourselves.
Sounds like the same results that occur in Chaos Theory with strange attractors. Galileo showed a pendulum ‘point’ out a circle in 24 hours time. But a Cray supercomputer came up with a design that looked like a maple leaf, as did the tracking of the eye movement of a schizophrenic. A definite phi-based word.
It is really awesome!!! I read about it in the Da Vinci Code(book by Dan Brown)
I want to make a model related to it and/or the fibbonaci sequence…
Can i get some help???
Class 10
Thank You
Pearl DD
Try the free models at https://www.goldennumber.net/do-it-yourself/ or check out the free trial of PhiMatrix golden ratio software at http://www.phimatrix.com. See also https://www.goldennumber.net/school-projects-interviews/ and https://www.goldennumber.net/golden-ratio-software/.
Phi is a magic thing surprised me from 3 years and it still do that .. Your conversions are very interesting .. I wish i could speak english better
ADDENDUM TO PANAGIOTIS STEFANIDES:
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In section 53, of PLATO’S “TIMAEUS”, PLATO speaks about the triangular shapes of the Four Elemental Bodies, of their kinds and their combinations : These Bodies are the Fire (Tetrahedron) the Earth (Cube), the Water (Icosahedron), and the Air (Octahedron). These are bodies and have depth. The depth necessarily, contains the flat surface and the perpendicular to this surface is a side of a triangle and all the triangles are generated by two kinds of orthogonal triangles : the “ISOSCELES” Orthogonal and the “SCALΕΝΕ” Orthogonal. From the two kinds of triangles the “Isosceles” Orthogonal has one nature. (i.e. one rectangular angle and two acute angles of 45 degrees), whereas the “scalene” has infinite (i.e. it has one rectangular angle and two acute angles of variable values having, these two acute angles, the sum of 90 degrees). From these infinite natures we choose one triangle “THE MOST BEAUTIFUL”. Let us choose then, two triangles, which are the basis of constructing the Fire and the other Bodies : One of these two is the “ISOSCELES” orthogonal triangle, the other is the “SCALENE” orthogonal triangle, its hypotenuse having a value equal to the “CUBE” of the value of its horizontal smaller side and having its vertical bigger side the value of the “SQUARE” of its smaller horizontal side. The value of the smaller horizontal side is equal to the square root of the GOLDEN NUMBER, the ratio of the sides is equal, again, to the square root of the GOLDEN NUMBER (geometrical ratio) and the Tangent of the angle between the hypotenuse and the smaller horizontal side is also equal to the SQUARE ROOT of the GOLDEN NUMBER (Θ=51 49-38-15-9-17-19-54-37-26-24-0 degrees). By applying THE PYTHAGOREAN THEOREM, on this triangle we obtain a biquadratic ((fourth order)) equation:
(T^4-T^2-1=0, from, T^6 = T^4+T^2, via Φ^2-Φ-1=0)
from which we obtain the size of the small perpendicular (T) as the Square root of the Golden Number (T=SQR(Φ)).
It is concluded here that by “THE MOST BEAUTIFUL TRIANGLE”, PLATO correlates the four elements (UNIFIED THEORY) through the General Analogies of their sides (Fire, Air, Earth and Water), i.e. Fire/Air is equal to Air/Water is equal to Water/Earth, to T, where T is equal to the SQUARE ROOT of the GOLDEN NUMBER.
T = SQR ((SQR.(5) + 1)/2) =
The values of the sides of this triangle are given by surd numbers, (solution of a fourth degree equation). Reorganizing this triangle, we get another one with the same angle values, which has its bigger vertical side equal to FOUR (4), its smaller horizontal side equal to FOUR divided by the SQUARE ROOT of the GOLDEN NUMBER, and its hypotenuse equal to FOUR multiplied by the SQUARE ROOT of the GOLDEN NUMBER. (Four divided by the SQUARE ROOT of the GOLDEN NUMBER is equal to 3.14460551)
Using this value for Pi 4/1.27201965 [= 3.14460551 ] as the small side of an orthogonal triangle , 4 its bigger vertical and its hypotenuse 5.088078598, inscribing this triangle in a circle of diameter D equal to the hypotenuse then product of
Pi*D = 3.14460551*5.O88078598 = 16 . THIS IS THE CIRCUMFERENCE OF THE CIRCLE= TO THE SQUARE OF THE BIGGER SIDE 4*4= 16 = TO THE IS SQUARE’S PERIMETER.
Multiplying 4*D ==20.35231439 = AREA OG=F CIRCLE =Pi*[D^2]/4 =
=3.14460551*[ 25.88854382]/4=20.35231439.
So we get this Squaring of the Circle relationship, elaborating on PLATO’S TIMAEUS, and more we get it drawn by Ruler and Compass.
Up to now those who had rejected as insoluble the quadrature of the circle, or the squaring of the circle, apparently did not elaborate on this triangle, even though some attempted trying [approximately] using a similar ,but not the same, and not as fair triangle as this PLATO’S one [as my proposition], the MAGIRUS TRIANGLE given to KEPLER [ http://en.wikipedia.org/wiki/Kepler_triangle ].
For a more illustrative view of my work please refer to:
http://www.stefanides.gr/pdf/BOOK%20_GRSOGF.pdf
Regards from Athens,
Panagiotis Stefanides
There was once a certain man who lived in the 19th century named Eliphas Levi, or Alphonse Louis Constant in the original French. He was a writer on ceremonial magick who expounded many of the secrets of ancient mystery initiation in his writings. Mathematics plays a large role in this whole body of arts and practice, and I remember reading in his “Doctrine & Ritual of Transcendental Magic” that one of the chief privileges of the Magus is to prove the quadrature of the circle.
I want this guy on my side! I feel that 61.8% of all the problems in the world could be solved if math teachers had any clue at all about how the Divine Proportion connects all the Arts and Sciences resulting in the kindling of a roaring flame, the likes of which not even Socrates could have imagined!
Can someone tell me the difference between
Φ and φ and ϕ.
Thanks Again for the help on the models!!!
Φ is the upper case Greek letter Phi, which represents 1.618. ϕ is the lower case Greek letter phi, which represents 0.618, the reciprocal of 1.618. The φ symbol looks like an alternate representation or fonts for Phi. For more on this topic see “The Symbol for Phi” at https://www.goldennumber.net/phi-symbol/.
The Disney logo looking last phi symbol, the letter ‘j’ in the Symbol font, is from an older Greek alphabet, I believe, but still very ubiquitous ;^ )
Get somebody to measure the length of their hand.
Then get them to continue the sequence: 1 2 3 5 8 13 21 (last two added)
Let them pick any number from the sequence, divide by the number just prior (= 1.618 ish the higher the better approximation)
Times the length of the hand by the answer, get them to measure their forearm (elbow to wrist) and watch the reaction….!
Awesome!
This is a demonstration using your hand: Your thumb sticking up represents the 365 ft height of St Paul London your index finger represents the length of ST Paul 555 ft located at 52 deg lat approx.
Now take your index finger and point it up, it is the Washington Monument 555 feet on April4/5 at 12:00 it cast a shadow 365ft represented by your thumb. This happens at the co latitude 38 of London 52 =90
There was a reason Wren designed and built all of the churches and the first ones in America. Not positive of exactly why he used this method of demonstration but he certainly built them all using PHI.
Some of this info can be found in the three book by H.S. Stewart .If you can still find a copy start with; GEOMETRY IN MOTION
And check out the George Washington Masonic Memorial in Alexandria, VA. Identical to the Pharos Lighthouse in Alexandria, Egypt and 16.18 km up the Mt. Vernon Trail to the CIA HQ, Langley, VA. The same distance from Memphis Temple, Egypt to Heliopolis, and 1/10 the distance to Alexandria, Egypt from the Memphis Temple with its’ nearby Giza Pyramidal Complex.
ISLAMIC signal 1.618 THE GOLDEN RATIO!!!! (See video referenced at page on the golden ratio of planet Earth). Kaaba. Mecca. Hallelujah Lord. Does this signal clear or you do not want to surrender to ALLAH. God have mercy on us all.
An interesting video indeed, but subject to some interpretation as discussed here on the Golden Ratio point of the Earth.
that video (see Golden Ratio of the Earth page) was both wrong and scary.
I believe in the power of math to explain our universe. The kabbalah is another stream that adds a rational way to explain what is greater than us.
Kabalah is written QBLH in Hebrew and its value is 137, the golden mean, 0.61803 of the 360 degrees of a circle. Kabalah, Kaba Alah, is the philosophy of the energy of the universe. Kaba ist the Cube of perfection, the cube of the 26 dimensions and Al LH, ist AL, everything or God, and LH is nothing, simply the Nothingness in what all becomes by God. In today’s times we define the Atom in 3 aspects, Nothingness, Resonance and Gravity, NRG, Energy, the ancients wrote the Kabalah with a trivial mind, what means that all you read in sacred texts has 3 significations, a neutral one, a positive one, and a negative one, hidden in one single metaphor, symbol or number, thus we have the word, the letter symbol and the number. God is GDH, 345, the numeric value of MShH, Moses. If you separate MShH by the letters of air, Aleph, value 1, you get MaShAh, the Messias, value 31415, the thought of GOD in the creation. GDH of the ancients is equal to NRG today, energy. If you see Theos, Zeus in greek, and you see how he is depicted, you see a man with lightning in his hand, he is GOD, energy, and he powers the lightning bolt, male penis. All is about to know what the symbols tell you. That is why Hebrew and Greek Texts in the Bible and Arabic in the Qu’ran seem to be rubbish and non-sensed. Unless you know the Kabbalist Slang, the symbolism and numeric coding, those books tell you nuts, all is hidden behind the veil. Bible is a setup of 72 books, the 22 lower letters of the Hebrew Alphabet written in trivial cycles, thus 22 x 3, and the 6 sophitic ending letters, what are 6 books of theurgy, thus Goethias. It are indeed 6 and 66 books. It is the number of humans and of the beast, and the number is 6 and 66. 6 is related to the letter Wav, thus 666 is WWW. That mans simply 0, -, +, the trinity of energy.
The Golden mean in transcendent, the sequence is variable, and the growth of the human body corresponds to a sequence of 1 + 0.666. The Kabbalah reveals those secrets. Some will now say that this is not true, but Einstein said that the universe is infinite and endless, until someone came and proved to him that it is finite and has a beginning and an end, like all. We are all submitted to the law of St John, Scorpio in Zodiac, the symbol of death. The letter is X, X-Tos, Christ. X tells us that all lives and dies at same time, one beam is the way you go, the other the time that limits this way. You find this symbol as the crossed bones under the skull, symbolized by the numbers 3 – 22, you find that symbol as the propeller of the windmill, that is why you fight against windmills when a fight is hopeless. There are only 3 values in the structure of the universe, 0, 1 and Pi. The highest value of infinity is the Alpha Finestructure constant inside the Hydrogen Atom, the God particle. Do you know that the alpha Finestructure Constant rate in the atom of Hydrogen, defined by Alfred Sommerfeld, is 1:137. Pauly spent his life to find the signification of the number 137, he never found the explanation, he died from pancreas cancer, aged 59, in an Hospital In Switzerland, room number 137. Coincidence, nothing as such exists, universe is causal and effective.
I will not open to you all the wisdom of Kabalah, it would take years to tell you what is written in there. I am just a newbie, only 53 years of learning the wisdom of GOD, that is a minute compared to the 6000 years it took to write 32000 scrolls that contain this wisdom. The oldest symbol of Kabalah is the Sphynx in Gizeh, it has 40000 years of age. All religions, all cults, all myths are based on the same teaching and philosopy. The story is the same, the symbols are adapted to the local needs. A true Kabalist can go in any ancient ruins of any cult and read what the writings on the walls, the shape of the buildings, the geometry of the divine, tell him. There are no secrets in this world, there are only blind man.
to אָדָם אַבְרָהָם, this is not just islam which points to this number, every great structure on earth, the pyramids, the tag mahal, the universe, the flowers, the human body, everything is constructed acording to phi, its not just islam, every relegion points to this. in the bible, refrences are to to this number. jesus told moses to make structures acording to specifications, and they lead to this ! 1.618, PHI !!! this is another way of saying that every religion is the same. anciens knew it, egyptions, jains, hindu, christians, everyone , da vinci. every beautiful thing follows the divine proportion.
Harsh makes a faulty assumption. To show that some element exists in every religion does not make every religion the same. His reasoning is tantamount to saying that since every animal has blood, all animals are the same.
isn’t this exactly the point some would make? Since God (which God? mine is better than yours?) made everything and everything is subject to the golden ratio, isn’t everything the same?
God is God, and what we think or believe doesn’t change Him. It’s not that one person’s God is “better” than another’s but rather that one person’s understanding of God’s nature may be closer to the truth. Jesus said, “I am the way and the truth and the life. No one comes to the Father except through me. If you really knew me, you would know my Father as well.” Study scripture. Study those whose lives demonstrate closeness to God. Learn from the spiritual experiences of others and pray to God to reveal Himself to you on a personal level. Religion only has true meaning when it is based on a personal relationship with God. My personal experiences are shared at Snapshots of God.
the deeper you look inside of them, the more you will see that they are, even if to your eyes, the program projects a different image. Nothing is the way it appears to you. All you see is made by atoms, and all atoms are in depth made with the same things too. What differs is the resonant frequency and the gravitational magnetic forces in each of them. The resonant frequency determines the image you see. Those received frequencies are transformed in your brain to give you an image of what you see. Colors do not exist, they are part of your brain’s basic program only. Some particles are stable and barely change, some do, when gravity changes, resonance changes with it, the whole collapses and the aspect changes. Your body turns to soil and bones, uranium ends to become lead. The killer fact is time, time destroys all. We are all nailed on the 2 beams, one is the way, the other the time that limits this way. So, think that the faster you run, the faster you reach the end. So, take it easy and study the rules.
I first became aware of Phi long before I heard of Fibonacci, I happened to divide 1 by 1.6 and noticed it was kind of close to .6, I went on from there, trying 1.62, 1.618 etc.
Later i learned of Fibonacci’s 1,1,2,3,5,8 etc., but then found that the two starting numbers are irrelevant. Take ANY two numbers and add them together to get a third, then add either of the first two to the third, then continue adding third and fourth, fourth and fifth and so on, as with Fibonacci. The further you continue the sequence, the closer the ratio of any number divided by the previous number gets closer to 1.6180339887 etc.
Eventually I felt silly when I learned that Phi is simply 0.5 + the square root of 1.25.
Yes, those are three basic ways of the many ways to derive Phi. Others though go on to grow in their understandings and apply phi to the arts, architecture, design and more. By analogy, what kind of music would the world know if musicians felt silly and stopped after learning that thousands of songs can be played with three basic chords?
Dears, Gary Meisner and Edward and others interesting in this subject:
You can refer to my website and find an article under the title of “A Modren Model for the Cosmos” in this article I fixed this matter that the shape of the universe(cosmos) is completely as a snail shape shape. Then it’s also based on Divine Proportion. It’s too much important!!
Dear Brothers & Sisters,
As it is demonstrated in the video clip on youtube, the evidence are morethan sufficient for the existence of The Creator or God or Allah for all what exist and all living.
As we find the golden ratio common to all life formes and even heavenly objects such as planets galaxies ext.. ext.. what do we find on our planet earth it self when it comes to the golden ratio? when we apply that same formular on the planet earth, our home… what do we find? we find a clear evidence, a message, a fundamental and more preceisly, at the Golden ratio of the planet earth we find a common place of assemble for all mankind for all human from Adam pbuh to the last who will be born as a Human. A common place for all who wish to say thank you to its one creator, one God, only one who can be worshiped. But all 7 million cannot be at tht particular place or position of golden ratio to worship its creator, so God provided with a solution for all man kind. No matter on which place or in which corner of earth a Human lives, he or she can easily find out which direction is the direction of Golden ratio of the planet earth is, and then worship him on that particular direction. See how merciful and easy our creator is? He who may belongs to the truth, who seek truth, the truth and the wisdom will be given to him by God. Jesus pbuh said you will look and look and look but you will not see. you will listen and listen but will not understand, For your hearts are too heard and too stubborn. He who is meek in heart will find the way to the father in heaven. So be meek in heart and search for God. God says in his book, if i see that one of you take one step towards me, i will come running towards you to meet you. So search for him, all over until you find him. if you search, he will take your hand and guide you on the true path which leads to him. For sure! Jesus pbuh said who ever knock on the door of who sent me, the door will be opened to him.
Dear guys, similarly if u divide the distance between your head and feet by the distance between your umblicus and feet,the quotient is indeed the GOLDEN NUMBER….it”s applicable for all humans,monkeys and many other creatures in the earth…
what a miracle….
I remember reading ” The Da Vinci Code ” as a pure detective novel. There I made two discoveries that really enhanced my faith in GOD, JESUS and the HOLY SPIRIT. These discoveries were
A~ The Fibonacci Sequence
B~ The Golden Number PHI
Powerful and riveting
I was looking at how people started looking at the golden ratio as proof for a greater being and drifting off into creationism. But the thing is out of every language, scientific law or theory that exists to describe the Universe, none can explain it better than maths. Many creditable scientists like Stephen Hawking, they reckon that maths wasn’t “invented” to describe the Universe but Universe itself runs on mathematical fundamentals, and that now we are finding these mathematical formulae we are finally realising the beautiful simple language of maths.
And in the words of Dr. Stephen Marquardt, “All life is biology. All biology is physiology. All physiology is chemistry. All chemistry is physics. All physics is math.” Math is the foundation, but the most important aspects of human existence – love, joy, creativity, for instance – are found in the spiritual side of our existence, for which the math-based physical side is just the stage for the play.
The planck length is 1.616199…X 10 to the -35 power in meters. Hmmm, that’s pretty close to phi (1.6180339…). I wonder if there is a relationship? The planck length is the smallest length there is without losing locality.
I think that phi is definitely a great number for no reason
A perfect website to search for facts on the Golden Ratio.
the information is awesome…
I wonder what it is in base 6? Or 12? Different number systems would have to give some interesting results. Perhaps a “Golden Base” could be found. Where Phi and Pi had a more obvious relationship.
If a man’s parts are of a golden proportion, 1.6180339887…, and a cubit is said to be the length from the tip of the fingers to the tip of the elbow; then One Foot is equal to .6666 cubits. Do you also agree that cubit is equal to 1.5 feet?
A number of sources say that a cubit is 1.5 feet, which would then of course make one foot equal to 0.6666 cubits. That fact, however, is not related in any way to the golden ratio appearing in the human body. For more on its appearance in the human body see “Life and the Golden Ratio” as well as the Human Face and “Human Body and Phi” pages.
You can divide an 18″ cubit into two A and B segments representing the golden ratio (0.618 and 0.382), but the resulting segments are 11.1246″ and 6.8754″, which then bears no relationship to one foot or 0.6666 cubits.
The Fibonacci sequence When added up in Mod 9 produce the same 24 digits, these digits are aligned to where 124875 is going both ways positive and negative the 1’s and 8’s are in opposite positions same as the 7’s and 2’s…5 vs 4…6 vs 3…this is not the whole set to understand the whole set you must see all 4 sequences which are
1 123 5 843 7 189 8 876 4 156 2 819-
1 786 5 279 7 753 8 213 4 729 2 246-
1 459 5 516 7 423 8 549 4 483 2 573-
336966393369663933696639-
All of them obeying the same design 124875 which is a the doubling pattern going opposite ways..the 174…285…369..always in opposition, its the same pattern going opposite ways predicting every multiple not just 1+174… same pattern backwards if it was 1+285… with the 1vs8…7vs…6vs3…5vs4… To understand more please visit my Facebook I’m also an artist trying to make it visually easier to see all of there interconnecting relationships and how that model proves over and over again which numbers are positive vs negative , Dustin Rader
so i was reading the davinci code pretty intresting book, when i came across this art were it talks a bout the phi number i was really interested so i decided to nvestigate a little more about it, then i came across with this wonderfull site were i can actually learn of something i want, not like in shool were all your taght are boring and dull stuff. anyhow i read quite a while , but the thig s i still not quite belive that god made ll this proprtions and that this numer is proof that He actually exists, however, i dont think is any coincidence either. really i am just very intriged and amezed of what i can discover and learn if i just read. i read a commen earlier were someone said he wish this subject was toaght in school, an i guess if i had been lazy and not read i would probably never find out abount thi for a couple of years, and i though about the amoun of things i am missing in this world and the amount of things i dont now, and i dont want to be this ingnorant person like evrybody i know were they dont see the big picture, they dont see that the world is bigger than one stupid party. Or how it doesnt matter whats your race or color of skin we are all the same and it really doesnt matter, for a while i actuallly thought…well really nothing matters and i really belive that nothing matters becuase at the end we all die… and if there is really nothing after death then… we really are nothing compared to the hole universe that is bigger than we can imagine.
i went a little of topic backthere and i guess i just dont want to miss anything… i want to meet people as inresting as was newton or einstein were really all they cared about was of discovering and showing the world to people…
JESUS and MOSES are a part of ISLAM…!!! They were the greatest Prophets….!!! But u cant point out the value 1.618 in any other religion except the True Religions i.e. ISLAM and Christainity…!!! I <3 BOTH…!
Andrea,
The koran says, “Say not that allah begot a son.” This is a clear denial of Jesus Christ as revealed in the Bible, which says numerous times that Jesus is the Son of the living God or the only begotten Son of God (John 1:14-18).
Any religion that denies the Deity of Jesus Christ has been labeled as “Antichrist” by the Bible: I John 2:22-26: Who is the liar if not he that denies that Jesus is the Christ? This is Antichrist; the one denying the Father and the Son. Whosoever denies the Son, does not have the Father. But he that confesses the Son has the Father also. Therefore let this doctrine remain in you, which you have heard from the beginning. If this doctrine which you have heard from the beginning shall remain in you, you also shall continue in the Son, and in the Father. And this is the promise that he has promised us, even Eternal Life. These things have I written to you concerning them that seduce you.”
Bible Christianity has nothing in common with Islam at all.
More Intresting….!
If u take square of Phi(1.618033989) it is equal to 2.618033989 which is 1+Phi
therefore, square(Phi)=Phi + 1
similarily, 1/Phi = Phi-1………….
which makes this number more unique and interesting,isnt it???
The Fibonacci has its uses in music as well, Tool incorporates the Fibonacci sequence into the title song from their album Lateralus. The music and lyrics follow the sequence (up to a point anyway). Good video on it here: http://www.youtube.com/watch?v=wS7CZIJVxFY
Here’s another example: my personal monogram perfectly fit to circles in a golden ratio:
http://dribbble.com/shots/926469-RJ-monogram-blueprints-2x
I’ve been using the Golden Ratio in my art for over 30 years. In my new role as the curator of the Museum of the Golden Ratio, I’d like to invite you to take a look at http://www.museumoftheGoldenRatio.org. If you’re an artist, designer or architect using the Golden Ratio, the Platonic Solids, Fibonacci Numbers and related geometric principles, please go to the virtual museum and click on ABOUT for submission instructions.
This blog has been giving information about latest different styles of architecture designs.
PHI: THE DELIBERATE CLIMB FROM NUMERICAL NUMBNESS
Thanks a lot for the info about the Golden Ratio….
Sirs,
I’m writing a booklet for our non-profit’s mission’s website. Please inform me as to whom I might contact to get permission to use that terrific diagram of the Divine Proportion in DNA I found in The Hand of God by Lanny Johnson, page 24. He listed this website as his source. Thank you so much!
P.S. Your website is F A N T A S T I C to all us who are in love with mathematics!
I am working on a small project and would like to know if anyone can create a graphic for me. I need a double phi spiral containing 360 circulambulations around a pivot. Thank you in advance,
Namaste, isana gaura das.
is your small project large enough to have a budget for this graphic? are you looking for tangible art (painting on canvas, i.e.) or intangible/digital vector or raster image? do you want to purchase exclusive rights or allow it royalty-free?
correct spelling: circumambulation
thank you!
Haribol prabhu, am looking for your mail, can you pls write to me sarvabhauma108@gmail.com tnx ys sarvabhauma dasa
Can you explain how phi is related to Fibonacci?
The ratio of each pair of Fibonacci numbers converges on Phi as you go higher in the sequence. See the Fibonacci sequence page for examples.
I wanted to ask a question about the Phi spiral and musical scales.
Can anyone help me figure out a perfect version of a musical scale which relates to the golden ratio, where it is not compromised by fitting in to the convention of 440Hz, or having to be rounded up or down to semi-tones?
I’d really like to tune a musical instrument to this, but I am not knowledgeable enough to work it out myself. Thanks a lot
See the A432 scale and connection to the golden ratio frequency of 162 at https://www.goldennumber.net/music/
thanks and i request to study in your college i hope you will reply through the above contact.thanks
I used it to place my TV at the perfect height between the floor and the selling.
WOW!!!!!!!!! This is so cool!
Phi may improve the quality of our (working) lives.
Phi may be applied for personal leadership and time management.
A day has 24 hours. This is a fact.
According to phi, this may be a ratio of 9 working hours (ideally, including commuting time) and 15 hours of free time.
Let’s break down both figures according to the formula
(Golden Ratio = ( 1+Sqrt[5] ) /2 or 1.6180339887499. A/B = (A+B)/A = 1.6180339887499.)
Working hours (9): 6 hours of productive time, 3 hours for travel, breaks, call of nature, chat with colleagues etc.
Productive working hours (6): 4 hours are highly productive, fully concentrated. 2 hours are moderately productive, where your concentration is diverted (phone, incoming mail, co-workers asking for your attention unrelated to your actual tasks, etc)
Free time (15): 9 hours of rest (sleep, meditation, contemplation) and 6 hours of activity.
Rest (9): Sleep may be 6 if you really use 3 hours for meditation and contemplation (not everyone is happy with meditation in his/her schedule).
Sleep (6): 4 hours of deep sleep, 2 hours of moderate/light sleep (dreaming).
Activity (6): 4 hours of conciously or planned activities, 2 hours of random activities
Good luck in finding your balance!
Great website!
Myron Barnstone teaches the golden ratio, or golden section as he calls it, to his art students. His students are amazing. Check out some of their artwork at http://www.barnstonestudios.com .
Hi, I just would say THANK to ALL of YOU,
Your web site is amazingly interesting, and just when I find it I improvvisly felt like a man in the desert, strongly thirsty with great need to know and learn all of it !
I entered in it like in a spheric temple of knowledge with all my been !
Thank you !
The Golden Number ….shows that our Creator is really perfect. We are fearfully and wonderfully made.
Thanks so much. This really helped with my Math project. It helped me to complete three-fourths of my project.
Fascinating site! I hope you don’t mind, but I referred to your page on music and Phi in my blog on the 440 Hz 432 Hz controversy, referred above. I did some simple calculations based on your work and found that, for the fifth to be at 161.8034 Hz (exactly 100 times Phi), the A above middle C need to be set at 431.4757 Hz, probably imperceptibly off from 432 Hz, but we do love precision. Thanks again!
I’m very happy to have the reference on your site, as well as to learn from the added information you have provided on this topic. Very good article, with great audio examples to actually hear the differences. Thanks much!
I’m mad about Phi !
With Phi, anybody will unscrew their soul, and elevate their life to Deity, Godness, to heaven, paradise… Jesus, Buddha, God, Krishna, Mohamed, call THEM as You want !
Phi, is the basical parameter of the creation, usefull to bulid the key, that associated with love, can open the doors of heaven !
I can bet my life that is true !
the Colors of Phi
Very cool idea. Using decimal numbers for hexi-decimal color codes though makes all the colors dark and muted because hex colors that begin with 0-9 only do not use the brighter colors created with A-F. Any ideas on a way to capture the full spectrum of color that still uses the sequence of digits in Phi?
Great stuff, guys. Wish I had more time – but only just found you.. More tomorrow, because I want to know if you’ve heard of Jantsch’s universal fourfold spiral pattern , and how – and if – it relates to the golden section, Phi, Fibbonaci series, etc.
Thanks, and great to find you. Salaama
Phi is pleasing to the all seeing eye.
Hey guys,
First I would like to say what a great site this is…I was very impressed.
I am sorry if there are already articles about it but I would like to know what makes a perfect office.
I have this theory that companies that are growing have office that contain many golden ratios in terms of office layout. (tables and chairs). There may be correlation between office layout and no. of golden ratio.
Has any research been done on this topic?
Thank you!
Recent experiences have prompted me to come here to emphasize …
A trick question: What is the square root of two? It is the number whose square is two. Full Stop!
What is Pi? It is the ratio of the circumference of a circle to its diameter. Period!
What is the golden ratio? It is one plus the square root of five divided by 2. It is not any of its decimal approximations.
It took me many years to appreciate the facts that I have just stated. The process of understanding began when, circa 1995, I typed Sqrt[2] into Wolfram’s Mathematica, which gave as output ‘radical 2’ – an exact symbol for the number – like Pi or Phi. These symbols, together with the precise definitions, keep us in mathematics. As soon as we state numerical approximations, we leave mathematics for physics, or engineering, or crafts – good things all but not mathematics.
When discussing these numbers that can’t be expressed as the ratio of two integers, people seem generally to feel a need to state or write down decimal approximations followed usually by … . Even wolfram dot com did this the other day on the subject of the square root of 1801. What they DID NOT SAY was that the square root of 1801 is the number whose square is 1801.
I asked a friend the other day “What is the square root of 2?” – after describing my interaction with Wolfram in the previous paragraph – and after saying it was a trick question. He said: “I don’t want to answer.” I answered: “It is the number whose square is two.” – See Rosenlicht, “Introduction to Analysis”, Dover republication, Chapter 2, Section 4.
Thanks for this great site!!
I don’t wish to be unkind or hurt your feelings, but not only is the “Biblewheel” idea completely false, but your attempt to apply this falsehood to yet another falsehood (Mormonism) isn’t going to work either. It is far from “harmless” as you allege. Falsehood is never harmless.
See this link for details on why the “Bible Wheel” idea won’t work, and also why the Golden Ratio format of the Bible is the only correct way to organize the Bible.
http://www.phibible.org/info/BibleWheel/BibleWheel.html
You may be interested to know that the Golden Ratio pattern of the Bible only works with the Traditional Canon of the Bible, that is to say, the 63 documents which make up the Traditional Canon of the Bible.
And because you cannot find the same Golden Ratio design in any other human document on the planet, it proves that the Traditional Canon of the Bible (which excludes the pseudepigrapha and the Apocrypha) is the only true Revelation of the one true God to mankind.
The “books of Mormon” do not have the Golden Ratio design; neither does the “koran”, neither does the bhagavad gita; neither does any other religious or secular book anywhere in the world: only the Holy Bible.
This is not a simple subject, so I recommend that you first download the Introduction to the Golden Ratio Format of the Bible here:
http://www.phibible.org/info/GoldenRatioBibleStudies/GoldenRatioBibleIntro/GR_Intro_Page_1.html
Also, you can visit this page which has a complete listing of studies that are freely available for viewing or download, which demonstrate in great detail how the Golden Ratio format of the Bible works, from the top level of the format down to the sub-paragraphs:
http://www.phibible.org/info/GoldenRatioBibleStudies/GoldenRatioStudies.html
May the Lord bless you as you seek the one true God of the Holy Bible through his only begotten Son, the Lord Jesus Christ.
Max Day
“Beloved, believe not every spirit; but test the spirits to see whether they are of God, because many false prophets have gone out into the world. By this you know the Spirit of God: every spirit that confesses that Jesus Christ has come in the flesh is of God; and every spirit that does not confess that Jesus Christ has come in the flesh is not of God. And this is that spirit of Antichrist, of which you have heard that it would come; and even now is it already in the world.” 1 John 4:1-3
The second link is not a download, but a place where you can study the same subject in photos in your browser.
There’s a circle-squaring “golden ratio” in a unique right triangle
where the hypotenuse has length equal to the circle’s diameter:
For D = 2.0 (also unique triangle’s hypotenuse) …
1.7724538509055160272981674833411.. long side, sqrt(Pi)
/ 0.92650275035220848584275966758914.. short side
= 1.9130583802711007947403078280203.. “Phi of Pi”
About “0.9265027503522..” …
Calculated with the Pythagorean Theorem
since 2(sqrt(1/Pi)) = sqrt(Pi)/(Pi/2) = 2.0/sqrt(Pi)
= 1.1283791670955125738961589031215.., constant ratio
of this triangle’s hypotenuse to its long side.
… perhaps, the new millennium’s tasty Two-Phi Pi
I think discussions about Phi appearing in nature and geometry is interesting. Discussions about Phi in art/architecture, definitions of beauty, and religion is boring nonsense. I don’t believe in gods, I think the concept is just people anthropomorphizing the universe or components/aspects of the universe. I also think the big bang is just another creation myth. I think it is pointless to debate faith vs. knowledge. I also think those who quote famous people on the subject are making an fallacious appeal to authority and have weak unimaginative minds, think for yourself, don’t parrot others. I think the universe is Phi and is infinite along all 15 axes. Note I say “I think” a lot because I don’t believe in anything. I especially don’t believe anyone really cares what I think, but I’m infecting your minds with my memes anyway, so there. :o)
“Thinking for yourself” is a good thing, but to “think” without appreciating and understanding the experiences and views of others will be a very “self-limiting” experience, won’t it? And thought without belief seems like just dipping your toes in the shallow end of the pool of knowledge and wisdom. Here’s an article I wrote on what I think: https://www.snapshotsofgod.com/thinking-outside-the-box/. The most personal growth I’ve experienced resulted from being challenged to see the world from a completely different perspective than the one I had held and accepted as fact.
Regarding the circle-squaring right triangle and “Phi of Pi” …
1.7724538509055160272981674833411.. sqrt(Pi), long side
/ 0.92650275035220848584275966758914.. short side
= 1.9130583802711007947403078280203.. Phi of Pi
= sqrt(Pi)/sqrt(4-Pi)
“Phi of Pi”, geometric evidence of another “golden rectangle” and a new design in this current study of Cartesian patterns of Quadraturial persuasion: http://aitnaru.org/images/Pi_Fork_n_Lute.pdf
sqrt(Pi)/sqrt(4-Pi) = Phi of Pi
= 1.9130583802711007947403078280203..
^2 = 3.6597923663254876944787072692565..
… and with geometric integration of 2/sqrt(Pi), circle-squaring right triangle and geometric signature of “impossible” Quadrature (the circle cannot be squared but squared circles exist … apparently).
Note: Difference of smallest and largest circle (and related objects) is Phi of Pi ^2
Dear Gary,
I admire your work.
Please, is there a way to construct a golden angle using a compass and a ruler? (without using protractor)
I didn’t find it anywhere and it would help me when working with children.
Many thanks from my hart.
Olga
Absolutely. That’s how it’s been done for thousands of years. I show two constructions, animated to show the steps, on my page at https://www.goldennumber.net/geometry/. There’s also another couple using circles for added interest at https://www.goldennumber.net/phi-formula-geometry/.
How kind of you. Thanks for the unexpectedly quick reply.
My English is not good enough – I still can’t find (or understand) the golden ANGLE, just the golden ratio. I guess I’m asking for a lot – where exactly can I read the description of golden angle of 137,51°? 🙂
Thank you for feeling me. I wish you all the best.
Olga
Appreciation about ” Nature by Numbers ?
Just came across this site and looking forward to reading it. Pity the comments section got bogged down by arguments about God from both the atheists and non atheists but that’s life I guess.
My question to Gary and anyone else is:
What about the other metallic ratios? How relevant are they?
Here’s an interesting article about them.
https://www.popularmechanics.com/science/a30714119/silver-ratio-math/
Hi Frank. Good question. I’ve not covered the metallic ratios in my research or writing, but they would certainly be worth an article on the site. In the mean time, here’s another good article:
https://rosettacode.org/wiki/Metallic_ratios
From what I see, they’re interesting as a mathematical exercise but I’ve not seen much in the way of meaningful application.
As site owner and moderator, that’s why I don’t mind discussion of the meaning of the golden ratio with respect to design in life and implications about the existence of God. Without that, it seems a bit like reading a book and discussing only its technical aspects of grammar, structure and style rather than the meaning and message of the story, and what knowledge and insights can be learned from the author.
Hi Gary, completely agree re: discussing the golden ratio and all its implications but I do get nervous because religious discussions can get a bit heated on both sides and in a way clog up any meaningful discussion I’m fine with those discussions as long as they add something and is not the usual trench warfare we see between atheists and non atheists.
Thanks for the link. I’ll have a look at it.
I’m with you s regards mathematics – I’m only interested in mathematics that is applied or abstract mathematics that can be applied such as the square root of -1. Von Neumann wrote an interesting essay called The Mathematician where he critiqued abstract mathematics which was interesting considering a lot oh his applied maths is based on abstract mathematics.
I came to the Golden Mean and your website through reading a book called The Golden Ratio which is part of a 64 volume series titled Our Mathematical World (published by National Geographic) which deals with applied mathematics but also discusses concepts such as Squaring the Circle.
I recently added the National Geographic book to my library. It has broader coverage than some books on the topic which are strictly mathematical, which is good. At the risk of being self-promoting, I’ll add that if you like that book you’ll likely like mine, which on Amazon it has hundreds of times as many reviews, at about 82% 5 stars. here:
https://bit.ly/goldenratiobook
Re the “usual trench warfare” I moderate every comment that is approved for publication on the site to maintain the overall quality, so I try to eliminate those that don’t add anything to the discussion or that take it off in a completely irrelevant direction. My choices won’t be the same as everyone’s, but this is not a site where people can just come and say anything and hijack the post comments for their own agenda.
Interesting link that has a good description of the metallic ratios. The latter part of the article is a little too advanced for me at the moment.
I found this very interesting video on metallic ratios and related ones. Much of classic Japanese architecture is based on the “Japanese” ratio (the sq root of 2). Also the narrator shows how a peregrine falcon uses silver (I think) ratio spirals to catch its prey. The advantage of using a spiral as it closes in is the falcon doesn’t have to take its eyes off the prey.
Metallic ratios (other than the golden one) on their own are not that interesting but when converted into spirals come into their own.
Good video. It makes the same point that I make in various places: Spirals in nature are generally equiangular (aka exponential or logarithmic) spirals, which is not the same as a golden spiral. This results in misinformation that leads to a lot of confusion about spirals and the golden ratio in general. See:
https://www.goldennumber.net/spirals/
https://www.goldennumber.net/nautilus-spiral-golden-ratio/
Re Japanese architecture and root 2, you may also be interested in this article on Orthogons:
https://www.goldennumber.net/orthogons/