Phi for “NeoPhites:”
Phi ( Φ = 1.618033988749895… ), most often pronounced fi like “fly,” is simply an irrational number like pi ( p = 3.14159265358979… ), but one with many unusual mathematical properties. Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation.
Phi is the basis for the Golden Ratio, Section or Mean
The ratio, or proportion, determined by Phi (1.618 …) was known to the Greeks as the “dividing a line in the extreme and mean ratio” and to Renaissance artists as the “Divine Proportion” It is also called the Golden Section, Golden Ratio and the Golden Mean.
Phi, like Pi, is a ratio defined by a geometric construction
Just as pi (p) is the ratio of the circumference of a circle to its diameter, phi () is simply the ratio of the line segments that result when a line is divided in one very special and unique way.
Divide a line so that:
the ratio of the length of the entire line (A)
to the length of larger line segment (B)
is the same as
the ratio of the length of the larger line segment (B)
to the length of the smaller line segment (C).
This happens only at the point where:
A is 1.618 … times B and B is 1.618 … times C.
Alternatively, C is 0.618… of B and B is 0.618… of A.
Phi with an upper case “P” is 1.618 0339 887 …, while phi with a lower case “p” is 0.6180339887, the reciprocal of Phi and also Phi minus 1.
What makes phi even more unusual is that it can be derived in many ways and shows up in relationships throughout the universe.
Phi can be derived through:

A numerical series discovered by Leonardo Fibonacci
Phi appears in:

The proportions of the human body

The proportions of many other animals

The solar system

The stock market
For an overview of key content of this site, read the article, Phi: The Golden Number by Gary Meisner, author of www.goldennumber.net and developer of PhiMatrix golden ratio design software.
jonathan says
The Theory of 0
First before all was thought.
There was nothing. = 0
If 0 then infinite
if infinite then all numbers
If numbers then separation or difference
if separation then equations
if numbers then lines = I
if pi then circles = O circle and line = Φ
it should be noted also that if you move the left half of the circle up touching on the line where the right half of the circle touches you get a wave. It is commonly believed that waves make up the subatomic particles. Just some mumbo jumbo in my brain. Hope this helps someone 🙂
DMac01 says
I got it Jonathan…. very good!
Madi says
Is this supposed to be a poem?
Michael says
♡
Justin says
Jonathan I already knew everything on this page but was looking for something more, your post was it!!! Thank you!
Nami says
Thank you!!!! Really helped 🙂
Wow… That was almost a complete paradigm shift. I have just recently started researching numbers again, as I had a thought years ago before I knew any if this. I wasn’t bad at math I just didn’t really try as hard as I could, but nonetheless; I had thought there were obvious shapes that seem to pop up all around the world and universe and quickly began thinking of geometry and math and discovered Phi, then my journey stopped as life got in the way…
Something has brought me back and I can’t help but feel I was meant to learn more and expand my horizon further. As any knowledge I can learn about the fundamentals, the absolute truths, and all that is seemingly ingrained into not only our surroundings and cosmos, but in the very vessels that allow us, the universe, the chance to experience itself. Your post did an absolute fantastic push in my new journey.
I think of how it screams volumes next to E=mc^2. Great mind.
“it should be noted also that if you move the left half of the circle up touching on the line where the right half of the circle touches you get a wave.”
I guess I extended the line upward, too, but I got a “$”.
The .”s” is actually a coil
Yes it is a coil or your fingerprint or the milky way galaxy or sea shell or infinity, though its the math behind it.
And just a share from my side its actually a great point to successfully trade in stock markets, as just find the High & Low on 30 mins candle, find its median, i.e dividing high and low by 2, add the percentage of golden ratio as profit target i.e .618% of the entry point i.e the median, and all done it will be achieved easily, and now just multiply the lot size though dont increase the target ratio as then it will be not a golden ratio anymore and thus it will be hard to achieve the target easily. Boom, if anyone tries just for fun sake even, MSG me on ujjwaljmd9@gmail.com, Thanks. World.
This idea sounds intriguing.
Will maybe try.
Thanks!
The Theory of 0
First before myriad things there was 0, or source, or infinite.
0=infinite
If 0 then unit=true & unit.id=1
if unit=true then unit.count=infinite
If unit.count=infinite then
enumeration of unit = numbers.exist & numbers.infinite = true
if numbers.infinite=true then unit.state.varriance=true & potential for unit.state.varriance=true
For unit.id=1to unit.id=infinite Do Until Step 1
enumerate unit.id
calculate potential for unit.state.varrience
Loop
Two different infinities are equal in size.
You make me wonder, is there any difference between any two infinities?
∞+∞=∞
Supposedly, yes.
Research Georg Cantor.
Be ubiquitous.
Infinity is comprised of an infinite subset of infinities. Some infinities are ?more dense? than others…. Take all integers as your base subset. The list is infinite. Now all even numbers. Also infinite, but half as dense? Are some infinities actually larger than others?
In Venn diagrams, there exists the idea of a “Super Set” of all possible sets. This would include all infinities, also. The Super Set is inclusive of all number in every form.
Mind expands to enjoy the Super Set.
Helen.
You might like to think of the following example?
The set of all positive integers ( 1,2,3,4…) is an infnite set.
If we use each element as the divisor and the number 1 as a numerator we get the set: 1/1,1/2,1/3,1/4… which is also an infinite set. The difference is that the second set fits into the space between 0 and 1 on a number line while the first set extends from 1 infinitely into spac ealong the same number line … and then there are the negative integers: 1,2,3,4 etc. (and their inverses)
Both the macro (outer) and micro (inner) universes are infinite and different as are the positive and negative ones and all are part of the Great Infinite One.
Wow… Your brain sounds pretty unmumbojumbo to me! Pure clarity – well, almost! 🙂
See also https://www.goldennumber.net/theology/.
your description is actually better than i think you realise.
it is a poetic expression of symbol. but actually has more mathematical depth than youve described.
You are smart.
Yes it is a coil or your fingerprint or the milky way galaxy or sea shell or infinity, though its the math behind it.
And just a share from my side its actually a great point to successfully trade in stock markets, as just find the High & Low on 30 mins candle, find its median, i.e dividing high and low by 2, add the percentage of golden ratio as profit target i.e .618% of the entry point i.e the median, and all done it will be achieved easily, and now just multiply the lot size though dont increase the target ratio as then it will be not a golden ratio anymore and thus it will be hard to achieve the target easily. Boom, if anyone tries just for fun sake even, MSG me on ujjwaljmd9@gmail.com, Thanks. World.
I didn’t get it, but apparently I am in the minority
I’m being reminded of a particular book/tom hanks movie here….
Yup, me too. The Da Vinci Code by Dan Brown. That’s what brought me here.
same
nuhu thats not true bro
Hello Johnathan,
I am experimenting with PHI and I have a question that I believe you can shed some light on if you don’t mind.
ovolbc@gmail.com
please reply
Thank you! This helped a lot!
very clever and very cool
Yes, it makes perfect sense. It’s interesting how the symbols so simply show everything.
Apply that to the Egyptian language hieroglyphics and see what you come up with
this is the truth as it was written in the Bible thank you for your comment
sweet
And we are taught this is all random the result of an explosion common man! Scientifically speaking: do we ever get order out of chaos? How many times do we have to blow up a junkyard of airplane parts before we have a jetliner or a singleengine propplain, The odds for success dwindle after each attempt? To improve our chances we blow up all the junkyards once. Will we get a Rolls Royce or even a pinto? CREATION demands a creator! The laws were set or created by prior knowledge, to deny it is only the result of faulty information or input.
It seems the more knowledge one learns the less wisdom they retain or can attain! “Wisdom is power, while knowledge is wanting.”
Finding that Schroedinger’s Wave Equation also uses Phi as its symbol, the link between waveparticle duality and the Golden Ratio may be right in front of us, and be pretty important in our understanding of how Nature really works (as the grail sought in the context of New Physics). https://www.quantumology.net/blog/fibonacciandphi
“if you move the left half of the circle up touching on the line where the right half of the circle touches you get..” a strand that looks strikingly similar to the nucleic acid double helix
But then again, I do have a wild imagination.
Sorry to finish your brilliant postulation; just couldn’t resist.
I have been working on an Angelic translator version of a 10 place system. The system is called “the DECHMA”
I have been developing this system for over 35 years, and I have perfected the portion of translation by which I have to day was by divine intervention.
I can say that your poem is very much on target, and I can show you the test of your equation in order for you to move on in either a quadratic solution or possibly a quantum solution.
Reply back for more info.
Oh no, no, no! You’ve got to explain further. What does the paragraph mean? WHERETHEHELLSMIKE@gmail.com
wow ive never read anything like this it helps so much thank you 🙂
Cool .. I see it..
Have a great day
Nice👍
Helpful,
Thanks!
Joe, really nice. Got lost at a point though.
Si la luz se propaga en medio de ondas…+ y dios es Luz… Las partículas sub atómicas son ondas… y todo crece a razón de Phi… ntonces….
Translation: If light propagates waves amid … + God is light and … Sub atomic particles are waves … and everything is growing by Phi …
Cant Understand Joe…..! Can anyone EXPLAIN….!
Consider the set Φ={1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,…,∞}
(Refer to this set when needed.)
How did we get this list?
Begin with 0. The 1st whole number after 0 is 1. We add 0+1 (and 0+1=1) <–Notice the last two numbers here are both 1 so we add them.
Adding them: 1+1=2
This gives us our next sum; so far we just have the set= {1, 2} a subset of Φ (top of page) so we're getting there…
We keep adding the last two numbers: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, and we keep the sums in a set = {1, 2, 3, 5, 8, 13} another subset of Φ
Let's keep going, last two above are 8 & 13, so: 8+13=21, 13+21=34, 21+34=55, 34+55=89, 55+89=144, 89+144=233,…etc.
Eventually we get the set Φ={1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,…,∞}
If we divide the last two numbers in the set, like 233/144 = 1.6180555 so this number, or ratio, "approaches" φ=1.6180339887…
I'll explain what I mean by "approaches."
We're going to start dividing the last two numbers in the set Φ
Look at 1&2 …Nothing special: 2/1= 2
Next 3/2 = 1.5 Ok, it's a little closer
Next 5/3=1.666… better
Let's skip ahead, 233/144= 1.6180555… which is approaching 1.6180339887… =φ
233/144 is the 1st ratio that gets us close to φ (within 1.618)
See how our ratio went from 2, 1.5, 1.666, skipped ahead, 1.6180555… and if we keep going, with bigger and bigger numbers the more exact the decimals become.
And we started at 0, right? 0+1, 1+1, 1+2, etc, so "as we begin at zero and the numbers get larger and larger they approach infinity, but our ratio get's closer and closer as it approaches φ=1.6180339887…."
I hope this helped.
this is so interesting.i was so good in math at school.i came across the phi when i read he da vinci code by dan brown and ever since iv become interested.thanks for this explanation.it has made it much easier to understand.
Use limits
Nor I, but he may be referring to the Temple in Jerusalem. Both the old and new were built/designed using this ratio. The sanctuary was the ultimate design ratio of phi. there may be other relationships, like the ark of the covenant.
Geometry can make it very, very simple!
All you need to understand Phi are the numbers 1 and 2 !!
If you draw a line vertically of length 2 and a line horizontally from the first lines base of length 1 and then join the two other endpoints with a line you get a triangle of sides 1, 2 (the two lines) and the third line has a length = sqaure root of 5 (thanks to Pythagoras!)
Add a line of length 1 to the longer line and draw a circle with it’s centre on the new combined line and that just touches the ends of this new line and you have found Phi!!!
Phi = the radius of the circle and has length Root5 + 1 divided by 2.
So all you need to do is know how to make lines of 1 and 2 and make a right angle ( 1/4 of a circle) between them add another 1 and divide by 2 and there is your Phi! 🙂
Easy huh?
Using this combination of one and 2 ( with a 90 degree ‘twist’ to it) Nature ( God if you will) creates a near infinite variation we see everywhere we look ( if we open our eyes somewhat).
You don’t need to be a master mathematician either. 😉
Thank you so much.
God bless you.
You can also use phi to calculate the circumference of a circle to within .04 of pi.
It’s probably more accurate than pi. Which pretty much makes pi obsolete.
Go the golden mean!
Finally, someone said it. We’re about to celebrate Pi Day again in schools all across the country, the real one this time, 3/14/15, which everyone and their brother is familiar with, but as just stated it’s rendered obsolete by the Golden Mean, Phi which no one or their whole family ever heard of! Way, way beyond mystifying.
it’s not actually the same thing. it can actually nit be obsolete since it is a different function and meaning altogether. This isn’t philosophical it is mathematical.
Love your point math is math! a simple yet complex subject of matter, not an idea, it works or it doesn’t.
Pi is defined as the ratio of a circle’s circumference to its diameter, so it’s not possible for any number to be “more accurate” for this purpose. Do you see why?
“PHI” UNIFIES ALL THING AND SUFFUSES ALL THINGS
Hi everyone
I’m in 10th grade and am doing my math project on Phi. I’d like to know if there are any applications of Phi that can be easily demonstrated to an audience that has never heard of it before. Also, is there anything I can make a scaled model of to show? The only materials I’ve got are thermocol and modelling clay. Please reply to this by 6th July
If you divide the distance from the tip of somebody’s head to the floor and the distance from their belly button to the floor, you get Phi. Same with from your shoulder to your fingertips divided by elbow to fingertips, and hip to floor divided by knee to floor. Another thing, take the number of female bees in a hive and divide it by male bees, anywhere in the world and you’ll get Phi.
Measuring people might be less reliable because clothes are a variable and you might want to keep those on for your project 😛
Source: The Da Vinci Code by Dan Brown
Same the only reason I’m on this site is because of da Vinci code I wanted to find more out about PHI
No you don’t. Try it. The ratio of navel distance to height isn’t phi. Try not to look for important truths about the natural world in fiction bestsellers.
Check your data. This isn’t based on a fictional bestseller. The navel to height ratio is very close to phi for many people, including myself. Even in his classic debunking article, Ph.D., Dr. George Markowsky measured his own family and found an average ratio of 1.63. Not everyone will have this ratio of course, but it’s not uncommon.
Why phi,,, now I get it
I thought Phi is only one Mathematics constant.
I can’t believe it is associated with so many interesting things!
Thanks for your share.
Go to YouTube and look up, “The Revelation of the Pyramids”. That’s where I ran into this ratio and was dumbfounded. Great documentary and informative.
i too have come to this site after watching the (brilliant) documentary “the revelation of the pyramids” . top film, id go as far to say its the best film iv seen in years
thanks didn’t know that…phi….is associated with so many things
PHI is the universal number for All life.
“Universal” means that it applies without exception to all cases, which to my knowledge isn’t true. More accurate adjectives would be “pervasive,” which means “spread throughout” or “dominant,” which means “main, major or chief.”
Right. unfortunately people can get overenthusiastic about something new, but most get the accurate picture at some point. Might take a college course in logic to get there though.
totally fascinated!!!!
same here
I have been very focused on sacred geometry this year. I have received much guidance regarding the creation of geometric forms and their uses. I love how numbers pull together so many different aspects of life. Like Phi and the Pythagorean musical scale. They are both about 5th’s. The relationship between 3 and 2.
nice!
True Dimensions of The Great Pyramid of Khufu… Base=777.03 ft, Height=480.24 ft… Calculated through Phi=1.618
.03 ft? That precise a measurement on an ancient crumbling pyramid is nonsensical. It would seem these numbers are especially doctored to fit the phi number. That isn’t too say that the ancient Egyptians didn’t know of it, but rather insufficient proof of it on its own.
Is it true that PHI is Gods building block.?
No. god didn’t or doesn’t need a building block, Also some religious practices do not have any sort of supreme being or eternal life. Buddhism for example. Go the middle way, I won’t try to explain that, bit look for a good explanation on line from someone better qualified than me.
Not all Buddhists are nontheistic. Google “Buddhist theism”, and “The Existential Buddhist” has a good discussion board, with primary source material towards the bottom. The topleftpointing swastika is the foursquare tetragram which represents the current pole star (Polaris) and the four positions of the big dipper (Ursula major). This is symbolic of the heavenly way of Life Eternal abiding in Jesus Christ. The way is for those who see Him unveiled, as well as those who see Him veiled, but believe it to be a mediator, as He came both to give life, and life more abundantly, by all, three measures of grace. Perhaps if this were better understood, things like the Chinese genocide of Tibetans would not be occurring. That is a number worth considering.
Thanks. A few of clarifications here. The four positions of the big dipper sp.( Ursa Major) is topright. Before it was used for infamy, the topright swastika was not only a Buddhist symbol, but it was the basis of the Basque cross, the lauburu. It appears to be spinning counterclockwise, which is the direction of the stars when one looks at Polaris. The topleft symbol may be thought of as God’s viewpoint from above. That symbol appears to be spinning clockwise. That is the same direction as the appearance of the yinyang symbol, which represents the motion of the sun and moon when you face away from Polaris. I call the overlap of these two symbols the Tetragram, from the Tetragrammaton YHWH, that is the YHawn inbreath, and the WHew outbreath of the power of God. Be thoughtful.
If i have words consisting numbers of 30, 40, 1 then how will i calculate that according to this golden ratio?
And what is the process of calculating this, im not getting this
To find the golden ratios of any number, just multiply it by 1.618 and divide it by 1.618. Golden ratio relationships with 30 are thus found at 48.54 and 18.54. You can round that to 49 and 19 if needed.
This mindblew me so good. I love the orgasmic effect it instigates in my mind. Truly a large phenomena, and will always be on my mind
I readthe male brain is a line
the female brain is a wave
viva la difference
which is language of the heart 🙂
Phi is amazing.But nobody in my year knows what it is.I’m 10.
Phi is much more than amazing. Nobody in my year knows what it is either. I’m five decades older than you. Just to show how amazing, I’ll give one example from my life that is happening right this second.. I’m a retired high school Social Studies teacher. I did my student teaching with a guy who is a Vietnam vet with 3 Purple Hearts, a three decade devotee of Parmahansa Yogananda and the SelfRealization Church, and my best friend. The city we live in, where he has spent practically his whole life, has a Central Ave. If you drop a location pin from a Google map app on a cell phone for 6180 N. Central it lands in the middle of avenue itself, right in front of my friend’s SelfRealization Church. The place he has been learning to be enlightened for most of his adult life. He was married there, and even renewed his vows there. But I can guarantee that he was never taught that his International Church, started almost 100 ears ago, has locations worldwide, with addresses, area codes, zip codes, phone number, etc., aligned as much as possible, whenever and wherever possible, with the Golden Ratio, the DIVINE PROPORTION, 1:1.618. How do I tell him? Do I tell him? Hell, I’ve been trying to tell the Administrator of this very website that his belief system is just as ensnared with the Golden Mean as my friend’s Organized Religion, as they all are. The belief system responsible is the oldest of them all; the Master Architect of the Universe, the ancient Egyptian god PTAH, Patron of Memphis, and of artisans and craftsmen, who built the Temple ‘Aeigyptos’ in its’ honor, and practically everything else ever since.
Very intriguing. I appreciate you sharing
Mr Hedding i suggest you 1. Read and learn the word of God YHWH and 2. Study history a bit better there are many deceptions and lies. Suggestion 1 is your best bet because if you understood Phi you would see it proves intelligent design.
Mr. Alan I suggest you 1. read and investigate just where your god YHWH comes from and 2. study what those originating people knew. Suggestion 1 is your best bet because if you understood where your beliefs originate, you would see they all begin with human beings who were in touch with the transcendent long before the dualism of your patriarchal mythology narrowed everything down to a “daddyGod” who commands you to love him. (btw: when has COMMANDING love ever worked?)
Only in the inverse
The ‘Da Vinci Code’ does wonders!!! Thank you @jonathan, it helped a lot!!
Occam’s razor=be brief
over lapping ellipses=symbol for empathy
there is a good orderly direction=a safe universe
🙂
Quite.
Excellent article about Phi. Me too, I find it interesting to know that its not only for Mathematics, it can be linked to numerous useful factors.
We named my son Phi after this equation.. No we’re not math nerds or philosophers, just appreciate things for what they are and knew my son deserved a unique name, however I wanted something with meaning behind it. A friend brought this to our attention after my husband wanted to name him Fi, after a Foo Fighters song (????), but i couldnt get down with the spelling. After studying up on this and discovering that not only is phi present in almost everything throughout the universe, we also came across the part that stated that Phi is hard wired in our DNA to influence how we percieve beauty, and furthermore, that doctors use these phi proportions during cosmetic surgeries BC it is such, and knew that this was the name for him, BC in essence, Phi = beauty to the human mind.. I have only come across one other person who knew where his name came from and what Phi is (a Dr at the hospital where he was born, go figure) but I enjoy explaining it in lamens terms every time we’re asked where it came from.
I also thought about the irony that he was also born in March 2014.. 3/14, pi. It was definitely fate for him to receive this name.
Pi is not phi……
awesome!!! 67 years old and learning things everyday. PHI is new and exciting for me.
kewlnumbers 🙂
formula for the spiral
the cochlea
the chambered nautilus
a spiral staircase in New Mexico
sea shells
the spiral modulus
we find what we know to look for–and lots more:)
I have always wondered if Phi in nature would occur outside of our own planet, or is it a force that occurs due to earth gravitational pull, orbit.
It’s not limited to the Earth. The rings of Saturn are reasonably close to a phi proportion to the planet itself. It has been found in quantum solid state matter and perhaps even time. See the articles in the Cosmology section of this site at https://www.goldennumber.net/category/cosmology/.
I found it, Mark!
https://symbiosissite.wordpress.com/2016/03/05/ifoundgodsintendedmessageencodedwithintheimpliedvaluesofournumbers/
I know all about the the Fibinacci Sequence but can anyone define how it relates to numerology if it does. I don’t know how it couldnt being everything in existence was created using numbers. Thanks ………..
how creation occurs to me is a mystery
Yes, there are many unknowns. It seems though that we can start with a couple of logical possibilities of how creation has occurred. We’re here because of:
1) A freak chance with no design or purpose, or
2) A life force of some kind that has driven the creation of the universe and the life within it.
If there is a life force, there are two more possibilities:
1) It has somehow created life forms (e.g., you) whose intelligence, emotions and awareness surpass its own, or
2) It has created intelligent beings whose human qualities are a reflection of its own greater yet capacities.
Which choices strikes you as the most rational?
#2 G Meisner (Occam’s razor)
I finally constructed a reply
like my experience
my truth is wordy
C S Elliot said “experience is a brutal teacher
but we learnGod do we learn”
I lile the interpretation following The theory of Morphic Resonance by Dr. Rupert Sheldrake Ph. D.
http://goldenfed.blogspot.com/2016/06/theeuclideanalgorithminexpanded.html
Describes how the Golden Ratio comes in an Infinite Variety beyond the mere quadratic 1.618 which we are familiar with. The Silver Ratio is similar as it can be geometrically implied. More on this latter distinction, later….
look up the golden ratio of the muslim kaaba or quran. you will be surprized at what you find.
You can read about it here: https://www.goldennumber.net/goldenratioofearth/
What keeps most of us in the dark when we talk about Pi, Phi, or any other equations; yet we don’t rightly secure balance our own speech. Live is temporary and subject to death & birth and Life is endless and exempt from death and birth.
It’s important first that we hearsee. Then we ahaaa moment, which we can seesee. That leads to speaksee and for some who are compelled to be impaled to teachsee. Ok, I know you like it better all cleaned up. So here it is:
Hear one, See one, Speak one, Teach one, Be one, Are one. All roads may lead to Rome, but all mathematically equations lead to “Existence is One”. And Philosphy, Science, Religion, Art, Music, Poetry,
and Knowledge to its unity leads to the same three words: “Existence is One.” So if you want it all, there it Is.
There is nothing else.
There is a lie in every belief, If you can proceed past the lie in your own BELIEF, not only will you not be prejudice, but you will know who we, thee, she and he Are; The I am . . . am I. This is
immortality, welcome to “It’. If this wasn’t so, I would tell you something else.
buckowens67@gmail.com
Beautifully written.
Hi everyone!
Sorry,I can’t understand how phi could be central part of all things in universe?
If it is possible who can be prove by picture or sth like that please
Thanks in advance!
abdullayevdavronbek@mail.ru
No one who really understands the topic would claim that phi is the central part of all things in the universe. It’s not. It is, however, a number with some very unique properties, and it appears in a number of surprising places. For a clearer understanding, see my articles at https://www.goldennumber.net/goldenratio/ and https://www.goldennumber.net/goldenratiomyth/.
There is something deeper about Phi and pi, nobody told it yet. The number 1,618 is merely a point that points out a location in the universal formula for all natural systems, called Matrix/DNA. It happens that this location is just where the force that is responsible by replication, or reproduction of things in the system, begins to reproduce the left face of the spherical formula, building the right face. Since the reproduction results into two equal copies, it produces de bilateral symmetry. It happens for example, when the DNA separates into two strands and each one strand replicates itself, resulting two DNA’s.
For understanding it you need see the universal formula at http://theuniversalmatrix.com . This formula was found when I was making comparative anatomy between living and nonliving system. Extracting the internal energycircuity of all natural systems I observed that it was resulting all times the same pattern. Big surprise was when founding that the formula is the template behind the building blocks of galaxies and the DNA, the fundamental unit of information.
Now we will understand Phi. This formula built all natural systems and then, we found it encoded into the general light wave resulting from all seven radiations in the electromagnetic spectrum. Here I found why there is the Fibonacci sequence. When the light wave propagates creating the seven layers, each new layer is longer than the anterior, just 0,,618 longer. So, each next layer will be the size of the anterior, which is the unit 1, plus 0618. Since that each layer has its specific size, frequency and vibration, we can see how the natural forces applies different functions, dynamics, to organisms, like the different sizes and functions of the different fingers in a hand. I am discovering lots of other things now, about Phi, registering it as articles in my website. ( if you see the Matrix/DNA formula, Phi is over F5, the reproduction function.
Maybe I missed it, but I didn’t see it. I found it odd this page doesn’t have the “exact” value of phi, which is (5^1/2 + 1) / 2.
I also didn’t see any mention of phi’s reciprocal, which I find rather interesting because it has the exact same decimal value as itself (truncating the leading 1 or 0, obviously):
phi = 1.618033988749894842….
1/phi = 0.618033988749894842….
Anyway, just wanted to point out some more phi fun facts 🙂
This site has over 100 pages devoted to the golden ratio, so this page is just an introductory index of topics. If you click on the Mathematics link on this page it will take you to the information you mentioned. See https://www.goldennumber.net/math/
The number Phi is the mathematical representation of the natural force responsibly by all reproductive processes and events in Nature from stars systems to human bodies. Every time everywhere this force is present, and when Nature organizes matter into systems, if the systems has the tendency to selfrecycling it is this force that does the job. The most common presence of phi is at spirals. Why is there phi in spirals? Because a living spiral has the tendency to selfexpansion, and for doing it needs to reproduce the last circular wave into a new wave. Who help grabbing the shape, constitution, etc., of the last wave and projects its ahead into empty space? Phi.
Once time – at the origins of life – there was only RNA, no DNA yet. RNA was not a complete and working system, but, when the force of phi acted upon it, the RNA was fixed as left face and the left face was reproduced as right face. Phi is force that came and go, it does not belongs to systems, it is temporary, responsible by cyclic processes. Then, cyclic menstruation, lunar cycles, etc. For acting in matter, this force needs to build a material tool, it is condensed into matter/energy. So, for acting upon RNA it build the Uracil base and after the reproduction it was retired, DNA has no Uracil. DNA grows by making and adding new building blocks. So, the force comes again ( maybe with help from RNAuracil) and reproduces the last building block.
Ok. Nobody never told or published the suggestions above, so, how I arrived to this conclusion? I am the author of natural’s systems diagram/formula, a pattern that I saw ( first time in Amazon jungle), flowing as the circuit of energy/information that runs inside systems. From atoms to galaxies to cells to human bodies to brains: all are copies of a unique template system, universal, which we represent as a simple software diagram, it is at my website. The flow running inside is represented by parts (particles in relation to space) and arrows ( waves, in relation to time). About Phi I discovered it in the formula when measuring the scales of the circuit, then, there was a systemic function located at a point that resulted into 1,618… Studying the function and grasping all traits, I arrived to Phi definition above. But, take care: I am not the owner of thru, I have merely a new theory, which is under testing, so, I am repeating that it is not a scientific theory, but a philosophical one. You must have yours conclusions.
A few thoughts to add to this. Most spirals in nature are equiangular spirals, meaning they expand at a constant rate. This property, however, does not mean that they have anything to do with phi. A golden spiral based on phi is a very unique example of an equiangular spiral. You say that the “force of phi” acted upon RNA, but how is phi a force? It is a number, a very unique number, but still a number. The “force”, if not one of the recognized forces like atomic, magnetic or gravity, must have been something else, perhaps a life force or even a creative force that we have yet to be able to measure scientifically.
Gary, if you don’t see the natural formula that nature has applied for organizing matter into working systems (the formula is at my website), you will not understand. Nature has the “project” of the best perfect working system – which is a motor continuum – but this system at the most optimal state does not exist here, it is like a dream goal for the future. We use the formula as this optimal state as a template for comparison with all another natural systems, because this method reveals where a system is not perfect, has a problem, etc. Then, the optimal system is totally complete when has seven systemic parts, each one performs a different function. So, when I said in the post above ” the force”, I am saying “the function” ( sorry, my mistake). All functions has a precise location in the systemic circuit and we found the number 1.618… just at the location of Function 4, the function of reproduction.. This number remember phi in Math, so, curious, I went looking for what and when applies in real things and considering that the at the universal formula this number is exactly upon the function of reproduction. This function produces bilateral symetry when reproducing the left face into a right face, the left strand of RNA into a right strand creating DNA, etc. Bi lateral symetry is the secret of beauty in Nature qhich is merelly an effect of a function, or a natural force, that is coming since the Big Bang building systems. But I understand that you can’t not understand only with my words, this issue is very complex because humans never saw the world by this perspective, compilled into Matrix/DNA Theory. Cheers…
(Note: the following uses highend UTF8 characters for different forms of the Greek letter “phi”. If they aren’t rendered correctly this may prove to be a pretty confusing post.)
In terms of nomenclature, I think it’s worth alerting readers to the fact that they’ll quickly run into differences about which symbol to use for this constant, 1.618…, and its derivative, 0.618….
Here, you’re using the uppercase forms for the bigger of the two numbers…
Phi = 𝚽 = 1.618…
phi = 𝛗 = 0.618…
I’ve also seen this usage at http://www.ebyte.it.
On other sites, usage is reversed…
phi = 𝛗 = 1.618…
Phi = 𝚽 = 0.618…
I’ve seen this usage in two Wikipedia articles and in the Khan Academy videos on YouTube.
I’ve even come across f = 1.618… on http://www.numericana.com.
What adds to the potential confusion is the similarity of appearance, depending on the font used, between the upper and lowercase forms of the Greek letter, for example, Φ vs φ. It’s best practice to use this fancier version — 𝚽 — for the upper case and the looping form of the lower case — 𝛗.
In terms of which nomenclature to choose, I do like the easy association of the uppercase letters with the bigger number, but to me, Wikipedia represents a general consensus that makes it authoritative, so I would tend to go with 𝛗 = 1.618…
Sorry, for my example of confusingly similar forms of the upper and lowercase letters, I meant to use this pair: Φ and φ.
I apologize for any confusion 🙂
People should stop talking about god when they don’t know the first thing about the world they live in. How can you know and imagine a god when you can’t even understand whats in front of you?
Clearly all of this is perfected in billions of years, and all based on rules and laws that governs this universe. Evolution of life on earth is the best example. How it started and how it is still evolving to something more, it tries, it learns and updates the code for next generation.
No one can imagine a higher being because we are so limited and insignificant! So please stop. Instead try to live, survive and advance based on your intelligence (being good is essential for survival for humans and earth). That’s our goal in here. If you follow these fundamental rules the world becomes a much better place.
And if, if there was an afterlife and a judging god, you’d be proud of how you lived your life, the way nature and evolution intended it.
Hello RR. I know you’re very sincere in your good appeal, but your arguments are not well grounded in logic or knowledge of the spiritual side of the human experience. Perhaps we’d better understand the world we live in if we sought more after the One who created it. If we’re completely honest, it’s really not all that clear that the wonder of life can be explained by evolution. Evolution doesn’t even explain the origin of life from inanimate matter. It just explains changes in already living creatures. And why do the laws that govern the universe exist as they do, and why are they so precisely tuned to support life?
YOU say we can’t imagine a Higher Being. By contrast, Jesus Christ said, “If you really know me, you will know my Father as well” (John 14:7) and “So I say to you: Ask and it will be given to you; seek and you will find; knock and the door will be opened to you.” (Luke 11:9). YOU say live by your own intelligence. By contrast, wisdom from Proverbs 3:5 says “Trust in the LORD with all your heart and lean not on your own understanding.”
There are deeper experiences. answers and insights at your fingertips, but to find them you have to step outside the boundaries of the beliefs you have accepted that keep you from seeking them.
I had no idea that Phi and phi were different
thank you kanye, very cool!
I’d like to figure out how to incorporate this into gambling so I can reclaim all my losses at the casino
See my section on gambling in the article at https://www.goldennumber.net/fibonacciseries/. The short answer is that there is no way to use the golden ratio or the Fibonacci sequence for a surefire approach to gambling. All gambling is based on chance with statistical probabilities, and the odds are calculated in advance to be in favor of the casino or lottery. Even if you place bets on every possible combination, you’ll lose.
I need to know what is 1.618 as per da vinci how we measure human body as per da vinci.
Leonardo’s most famous illustration that “measures” the body is that of Vitruvian man, and it is based on the measures described by the ancient Roman Vitruvius. See my article at https://www.goldennumber.net/leonardodavincigoldenratioart/ for more on this.
1.618 is the usual ratio for the human eyes field of view, that why when human creates something or find something attractive they unconsciously refer to phi!
Everyone’s arguing if phi proves gods existence. Well, it both “ does” and doesn’t. I thought it was obvious to everyone by now that ,living in a reality that is so easily described using math and numbers, we are almost certainly living in a computer simulation. All the problems religion and science run in to when explaining our existence are effortlessly brushed aside if you view reality as a virtual construct.
Can I email you?
Remember the God of Baruch de Spinoza, and you will be not very faraway from Einstein footsteps.
Or God is a mathematician and understands it all bc he made it all. How funny for our God to drop such beautiful clues to his mind in our tiny, REAL, 3D world (any mathematician/programmer will giggle at how small 3d problems really are in application) . If we live in a program, who wrote the code? If we live in a program, how come we feel love and the best AI we got cannot. It can predict feelings based on linear optimizations AFTER training bc we, humans, tell it it’s love… but even babies know more of such things than programs ever will. God is a mathematician bc he made it and mathematicians are blessed to get a minuscule insight to such understanding. I’m a mathematician and I believe in God. *gasp
Phi is pronounced “Fee” NOT “Fie”, as Pi is NOT Pie, but Pee! Despite modern interpretations, I believe we should be trying to be striving for accuracy, not convenience. Thus, for example, Americans do not speak “English” but “American English,” Australians speak Australian English, etc. Whether you wish it or not, there is a difference, so please can we begin to aim for correctness please? Before anyone starts to criticise me for my stance, I’d like to point out that I do NOT speak “Queen’s English” as I am in the North West of England, so I admit I am not perfect. So am I a pedant? Probably, but I am sick of our language being abused by other nations who then claim to speak “English” when they obviously don’t!
Interesting point, but does “proper” English of today even sound like the English of the 1600’s or the English from earlier times yet. So if you want to aim for “correctness,” you have to define the standard and then also establish why that particular standard should be better than the possible alternatives. By the way, do you know the most commonly spoken language in the world? It’s broken English. Arrgh.
Sir,
I have recently published a paper that reveals THE EXTREMELY PRECISE Pi:Phi CORRELATION, which is firmly premised upon Classical geometric principles.
Video Link: https://youtu.be/P1Ddz55JFlc
Paper Link: https://rajpub.com/index.php/jam/article/view/8498
Regards
Dr. Chetansing Rajput
chetansingkrajput@gmail.com
“Plank Length x Phi”
The 3 Radii of Hydrogen
1.61252 10^35 meter x 1.61833989 ^116 = .282537 angstrom
1.61252 10^35 meter x 1.61833989 ^117 = .457154 angstrom
1.61252 10^35 meter x 1.61833989 ^118 = .739691 angstrom
The two wave lengths required for photosynthesis
1.61252 10^35 meter x 1.61833989 ^136 = 427 nm
1.61252 10^35 meter x 1.61833989 ^137 = 691 mm
The most prevalent angle in nature
.618 x .618 = .382 x 360 degrees = 137.52
The Fine Structure Constant
1/137
is 1.619 still considered a golden ratio?
how much is the term “approximately” ?
because I am currently researching on golden ratio and assume ratio with only + o.05 difference is still considered a golden ratio, however my teacher rejects this assumption so I need a research paper that supports my assumptions
There is no one hard and fast answer to your question. The amount of acceptable variance could depend on a variety of factors. One would be the size of your sample, and a sample size of 30 is generally considered the minimum for a statistically significant result. Another factor would be whether the observations were in something where the golden ratio might reasonably be expected to appear, such as in biological systems or in the works of an artist who was known to use the golden ratio.
When I do my digital image analysis with my PhiMatrix software, I generally like the variance to be only a pixel or two on images of anywhere from 600 to 6000 pixels, so that would be a variance of only +/ 0.003 to .00016. If your suggested variance of +/ .05 is meant to indicate a range of 1.568 to 1.668 then I would consider that much to large a range to still call the results as golden ratios. A variance of +/ 0.005 would in my opinion yield more accurate conclusions.
On the other extreme, some will tell you that nothing can be the golden ratio because it has an infinite number of digits. While theoretically correct, it a ridiculous position to take in real world applications because nothing can be measured with infinite precision, nor is there a need for it to be. If I use a golden ratio on a design on my computer screen with pixel level accuracy, it’s still a golden ratio in concept and in application, and the exact golden ratio will fall within the golden ratio dividing line that I have created. It’s just a question of how much accuracy I need for a particular purpose.
I’d recommend you look at other studies in the field of your study and seek to achieve results of similar accuracy. My book, available at https://bit.ly/goldenratiobook has a more detail discussion on your question. Your might also find these articles to be helpful:
https://www.goldennumber.net/goldenratiomisconceptionsbygeorgemarkowskyreviewed/
See the section “Flawed assumptions can lead to flawed conclusions”
https://www.goldennumber.net/goldenratiodesignbeautyfaceevidencefacts/
Phi=(1+sqrt(5))/2
I don’t understand why it took me so long to find this out. This should be part of the basics.
also
Phi squared=(3+sqrt(5))/2
Imagine the number system of ‘base phi’…
I use a simple way to obtain the Phi number:
Phi = (Sqrt. 1.25) + 0.5
In the book as well as the movie, “Contact”, because of it closer relationship to the five pointed star and the dodecahedron, PHI should have been noted over PI.
You forgot to name the most interesting Golden Proportion of Φ :
∏ = 4/√Φ
(seen at You Tube :The Non Transcendental, Exact Value of π and the Squaring of the Circle 1)
The derivation of Pi based on ∏ = 4/√Φ gives a result of 3.14460551102969…, while the standard accepted value of Pi is 3.14159265358979.., a difference of about 0.1%
There are a number of sources who are making the case that this geometricallyderived value of Pi is more accurate than the traditional value of Pi, which has been derived through calculus, limits and other methods.
I’ve not been able to prove the 4/√Φ value right or wrong myself, but anyone using referencing this calculation should be aware that this does NOT produce the traditionally accepted value of Pi.
These sources never showed a mathematical proof for their claims. Those being mostly esoteric groups, claiming secret knowledge from ancient writings.
Notwithstanding, there is a simple demonstration of the exact value of ∏:
We set a circle of D=1 and a Square of the same perimeter=∏
4b=∏
calculate the areas, using 4b as ∏:
Ac=4b*r^2=b
As=b^2
These values we can use as the short legs of a right angle, to apply Pythagoras and find to the value of “b” or ∏/4.
We need first to find out the corresponding Hypothenuse for that triangle.
The value of the Hypothenuse is “1”.
Why?
For this equation:
b^4+b^2=H^2
we can obtain any H value for any b value btw 0.707 and 1, respectively the side of the inscribed Square and the Diameter of the Circle. And btw those values there is the exact value of b or ∏/4.
The only choice for the value of the H is in fact “1”. Because, if we take any other value more or less than 1 we invalidate the premise for this derivation 4b=∏.
We would be working with another circle where b is no more ∏/4 or ∏ the perimeter of that circle.
Having explained why H=1 is the right choice, we can derivate the exact value of b and ∏:
b4+b2–1=0
b=0.786 or 1/√Phi
∏=3.1446 or 4/√Phi
This is the exact value of ∏.
“Exact” means, made out of one step or “act”:–> 4b=∏.
Ex–Act.
(many people confuse Exact with Accurate, which are two different concepts)
So, well. It is possible to square the Circle.