Just can’t get enough of Phi? Here’s a couple of ways to get as much as most anyone would ever need.
There are millions of places to find phi, but here’s some help in finding phi to a million places. You can download the PhiCalculator, a program provided free of charge by Alireza Shafaei. It will compute phi to the number of decimal places you specify, to 1 million and maybe more, and output the results to a text file. He’s also provided the C++ Source Code and a text file of Phi to 100,000 places.
Note: PhiCalculator was scanned with McAfee as of March 29, 2008 and found to be virus free but the user assumes all risks of use.
For those of you with smaller appetites, here it is to 20,000 places:
| 1.61803398874989484820458683436563811772030917980576286213544862270526046281890 244970720720418939113748475408807538689175212663386222353693179318006076672635 443338908659593958290563832266131992829026788067520876689250171169620703222104 321626954862629631361443814975870122034080588795445474924618569536486444924104 432077134494704956584678850987433944221254487706647809158846074998871240076521 705751797883416625624940758906970400028121042762177111777805315317141011704666 599146697987317613560067087480710131795236894275219484353056783002287856997829 778347845878228911097625003026961561700250464338243776486102838312683303724292 675263116533924731671112115881863851331620384005222165791286675294654906811317 159934323597349498509040947621322298101726107059611645629909816290555208524790 352406020172799747175342777592778625619432082750513121815628551222480939471234 145170223735805772786160086883829523045926478780178899219902707769038953219681 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Phi is cooler than Pi.
Why? Pi is embedded into the structure of the universe and nature more than Phi is.
No, Phi is in the structure of so many things in nature. Give me a list of things pi is embedded in in nature.
1. Pie
No further examples required.
Yes there is, just a food named after a number isn’t explaining enough (and it just happens to have a circle in it). There’s tau in there too.
Yes, you do have to explain. Just because it is named after a food, that doesn’t mean that it is explained. Although in is circular, there’s tau in there too.
Pie in spanish is foot
Geez, he was joking.
cells, planets, our eyes, basically everything that is spherical or circular in shape. (Approximately)
Just by circles, which you could use tau (radius to circumference). And in waves, if you are using radians, which come out of the distance on the circumference in the arc you use, (2 pie is the whole circumference), and tau makes a lot more sense there. (pie = 1/2 tau). What else are you thinking of?
Phi is the structure of life, art and the delicate fingerprint of life coming to reality against ALL odds(creator).(helps to understand the world)
While Pi is used in varies of mathematical solutions, some to help create and construct varies of things in 3D.(helps to describe the world)
Yeah! and PHI is amazing .. every breath we take every move.. every thought we make adds more digits to PHI.. Completely irrational.. changeable.. interactive .definable only in the experience. The exquisite ever-changing beauty of PHI is can only be fully expressed with one word.. ETERNAL !
but phi is in almost all of nature you see if you draw one shape and then you go an angle of phi you will never overlap completely so this is the best way of getting water/ sunlight/ food
+the symbol of phi looks like earth with a cross through it
also could someone tell me what that symbol actually means is or if it just looked cool
love sciency guy
If you go at any irrational angle, you will never get back to the beginning. It is possible that plant growth follows something like a golden spiral which would generate φ.
Phi is actually one of the Greek letters used in math.
another symbol is φ
> but phi is in almost all of nature you see if you draw one shape and then you go an angle of phi you will never overlap completely
Well that’s true but all irrational numbers have that property, including pi. Phi just happens to be the best at it
In The DaVinci Code, the golden number is expertly explained and it is rather fascinating.
I have read that and was truly fascinated. I must say I prefer the lesson known Phi, to Pi! A friend of mine can recite 152 digits of Pi. I am going to try to do the same for Phi!
Actually you don’t have to memorize it. When I use Pi in my artworks or to compose a password I just use a pencil amp and paper. It’s just simple addition.
I agree
i think phi is better
wholesomely agr
Yeah pi get boring but phi, phi never gets old.
Pi is just for circle and phi，almost every ‘golden’ (object)
Phi is coohler than Pi.
Both Phi and Pi are cool.
Pi is cool because there are six nines (999999) starting at the 762nd decimal place. Very strange to have such a long string of the same number so early in the sequence.
Phi is cool because it is so easy to calculate: (sqrt(5)+1)/2, so is base on the whole number 5. Also, if you calculate Phi to 100,000 digits, you will get six fives (555555)at around the 99,900th decimal place.
no e is better than both of them
So if you add all those numbers up and divided them by 20,000 would you get Phi?
No, the numbers are likely random and individually have no relationship to phi. If you add any set of random numbers from 0 to 9 and compute average you’re likely to get 4.5.
Heh, heh. This was posted on pi day.
I have just checked and the average is equal to exactly 4.50015
Good work! That confirms that the average of a set of random numbers from 0 to 9 is going to be 4.5. The small variance of 0.00015 is just statistical variation that will grow smaller and smaller as you add more digits to the sample population and analysis.
Does this also imply over a large enough sample size the number of digits that represent each number will be 10%? As in, 10% of the number will be 0s, 10% 1s, 10% 2s, etc.?
Yes, in an infinite string of completely random numbers, one would expect to find the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 each appearing 1/10th, e.g. 10%, of the time.
Yes, Phi is a H of a lot cooler than Pi
DaVinci Code??
I heard about this in the Da Vinci Code.
Now that is a great book….
I heard about this on Da Vinci Code too. When I heard about it I had to look it up because it sounded so amazing and now my brain hurts after browsing this website.
Actually you don’t have to memorize it. When I use Pi in my artworks or to compose a password I just use a pencil amp and paper. It’s just simple addition.
pi sucks because really the only thing it has a use for is dealing with circles. Phi is the ratio of everything: that’s is seriously awesome
Don’t be rude, ever heard of e^iπ=-1?
How about e^iΤ=1?
pi is incredibly useful… if you know anything about signals, which is literally everything in the universe, as our brains are basically sensory signal processors. From that we construct our image of reality. Look up Fourier Transform
Replace with tau. All of that was based on the wave that pie makes with sine (at least that’s the basics). What about Tau? It looks the same, just mirrored. It does the same thing.
Pi is more helpful in solving sums whereas phi is present in almost all forms of nature. Both of them are cool to me because of their unique individual characteristic…
I don’t think pi or phi is better or worse…
If we want to be really existential, think about this:
Numbers don’t care who is better. Numbers don’t make judgements.
It is the job of the mathematician to understand numbers. Therefore, a good mathematician would not have preferences for numbers either.
I’ll have to disagree with your logic. Think about what you’re saying, but in a different context:
“Viruses don’t care who is better. Viruses don’t make judgements. It is the job of the biologist to understand viruses. Therefore, a good biologist would not have preferences for viruses either.”
Ask any good biologist which virus he’d like to be injected with and I think you’ll find some very well defined preferences.
Yes Pi is circles but circles are nearly everything. Planets, stars, orbits molecular and galactic. Phi is Pi with an extra dimension time added, like a spiral is a circle plus time, a vortex is a spiral plus time, and a torus is a vortex plus time…
No explanation required.
But φ is still pretty cool, though. At least better than π.
Wouldn’t the C++ program run a little faster if you used ‘memset’ Instead of a for cycle to fill the array with 0s?
I look at the coad then I look at the comment… Guyz why you people are fighting with Pi & Phi?… When you don’t focus on the main necessity of this article… Btw… 2 are 2 kinds of used roshio… Thanx Admin… It will help me a lot… 🙂
I’m just sitting here laughing at the people arguing over whether pi is better or phi is better – and they can’t even spell pi correctly.
I just did some research on phi and this is probably the best website I found thank you
I’m trying to memorise digits of phi…I’m at 50, wish me luck!
Good luck. I’m at 213
I’m only on 40 D~¦
It’s just that people who are around me knows nothing about phi but knows a lot about pi………..I prefer phi better as its cool, but pi is as cool and awesome. 🙂
Langlands theory takes us from Grothendieck to a mathematical physics basis. Phi is the introduction to begin to compute the dimensional mechanics of space and time from the Hilbert program and learn the newer Brane physics.
Wowowowoowowooowowowowow
Pi is more helpful in solving sums whereas phi is present in almost all forms of nature. Both of them are cool to me because of their unique individual characteristic…
Pie is a food you cut and share… Now the Phi is the whole pie all 360 degrees of it .. And the people wouldn’t understand that portion they got cut of the wholetality without the center or prince of the Phi , dubbed pi . So God the whole of all gave himself and theoretical ending to teach man the signs of times to show the true meaning of Wholetality by creating a prince or end. They one and two do not exist until after the 6 8 are found and neither are found until 4 or 5 because no one new the 9th existed to truelly get to 10 , dimensions that is. Your mind is a lotus. Sometimes you have to die a little everyday to live a little. What better way than killing your brains cells by what they where made for, thinking. Your brain has more compactity than we use it for, but that’s be cause we haven’t learn realations is a ship of its own in a sea of its on. A ship that will never sail if you don’t unlock it. A sea that will forever run dry if you don’t drink and swim in its waters… God is whole. 360 degrees and one day man will be whole with him. Dimensions of the mind is just like the universe… They are the same from Atom on the Eve of creation. Nothing starts without three. Understand we got it wrong… Ters are not true they are real.. Imaginary is just important as real. God is true . A man can be true and real in the same mind. That’s why God created Us all four of uses… That way we could grow to the level where he could join all of Us and use our hands created after he seen the monkeys hands… Kappa phi sigma pi
The reverse function on lines 66 and 149 in the c++ file wasn’t in scope until I added #include . I’m using g++ version 4.8.4 on a Linux distro. I appreciate the code! Thanks!
#include < algorithm >
Wow. I can’t believe how many people are arguing about two simple irrational numbers. If you actually like either one, you would just learn about our and ect. You wouldn’t just spend your time arguing about two numbers that with both, with an equation, make beautiful things.
This is just my opinion on this situation. People are just arguing with other random people just because of two irrational numbers. It’s like going up to a random person wearing pink and saying, “HEY! PURPLE IS BETTER!” And just arguing about the two colors until sunset.
As an artist I come down on the side of Phi. It is found in everything from the Parthenon to the Mona Lisa and the Last Supper. It was not a man made concept but rather from the observation of nature. The nautilus, spiral galaxies, the proportions of the the human body and face. I utilize the Golden Mean in my own artwork.
Oh yes, it’s not for nothin’ that it’s often called the Divine Number or Divine Proportion.
e (euler’s constant or base of natural logaritm) is controling both pie and phi…
ha ha he he hu hu…
Phi (spiral) is Pi (circle) with an extra dimension time added, like a spiral is a circle plus time, a vortex is a spiral plus time, and a torus is a vortex plus time…
Sorry but it seems that this phi number is only accurate to the first 142 places. I wrote a Python program to check the accuracy of this number and it was fine for the 142 digit. After the sequence ….216269 the list of numbers here differs. Here is what my code generated.
1.618033988749894848204586834365638117720309179805
76286213544862270526046281890244970720720418939113
74847540880753868917521266338622235369317931800607
66726354433389086595939582905638322661319928290267
880675208766892501711696207032221043216269 72654306
56414640739624780407494551171076664365525976060013
32089764512620148275334237805965332764071218488345
I wanted all of phi
A perfect circle is a concept, it doesn’t exist in nature. Phi and its approximations are everywhere in Nature.
We know that the area of a circle is the radius squared x pi.
We also know that the volume of a cylinder is the area of the circle that it makes x height.
The volume of a deep dish pizza is as follows:
Let the radius of the pizza = Z and the depth = A
Then the volume of the deep dish pizza is the area x depth. Therefore:
Area = pi z² = pi zz
Depth = A
So, the volume a pizza = pi z z a
so?
Not So. Phi. It’s an acquired taste.
You say “one million” places, but the number of places is 100,000. This number is one hundred thousand, NOT one million! Oops! You should fix that!
The article says, “You can download the PhiCalculator, a program provided free of charge by Alireza Shafaei. It will compute phi to the number of decimal places you specify, to 1 million and maybe more, and output the results to a text file. He’s also provided the C++ Source Code and a text file of Phi to 100,000 places.” So you get the million places on your own with the program, not the downloaded text file.
wouldn’t phi day be on march 2nd and march 1st on leap year
I’m not sure which starting point you’re using to get to March 1 or 2. It looks like that would put the start at July 19. In any event, a leap year adds 0.618 days to the calculated Phi Day, so that would shift it from Day 225.58 to Day 226.20.
Look at where the Golden Ratio (Phi) point of earth is if you seek proof that there is a God. Then look at the book associated with the religion tied to that point and search for the speed of light being mentioned in this religious book. The book is Mathematically perfect and tells many scientific things some of which are recently being discovered.
Phi is what made me know God exists. I hope it can do the same for you.
Peace friends
See https://www.goldennumber.net/golden-ratio-of-earth/ for further discussion on this.
phi is a lie for it being in everything. people did a study and apparently no chose exactly the golden rectangle and it will never be accurate because it is an irrational number like you cannot make an exact circle because it will be a little off and you can basically put the golden spiral on everything without it meaning anything. check this for further proof https://www.fastcompany.com/3044877/the-golden-ratio-designs-biggest-myth. Overall phi is interesting but not in nature or in humans or any other place in real life.
Your information is incorrect, Alex, and the article you reference was incredibly poorly researched and grossly inaccurate. After it first appeared over 300 readers posted comments objecting to its contents, but then FastCompany deleted them all. I wrote a critique of the article in the first link below, and I saved many of those comments for your reading pleasure in the second link below:
https://www.goldennumber.net/fast-company-design-john-brownlee-golden-ratio/
https://www.goldennumber.net/did-fastcodesign-censor-reader-comments-on-the-golden-ratio/
Another rebuttal was written by Darrin Crescenzi, a highly regarded designer who is often quoted in FastcoDesign as an expert in the field:
https://medium.com/@quick_brown_fox/why-the-golden-ratio-matters-583f6737c10c
Much of the information in the article was quoted from an equally poorly researched as inaccurate article, which I critique here:
https://www.goldennumber.net/golden-ratio-misconceptions-by-george-markowsky-reviewed/
No one in the know says that phi is in everything, but to say it does not appear in nature or real life applications is inaccurate and misinformed.
Phi is the key to the ‘resonant interval’. If you don’t know what that is, see Marshall McLuhan’s “Where the Hand of Man Never Set Foot” (various sources). The Tree of Life is in the *midst* of the sensory garden, so it is the resonant interval or the interplay of sense. By eating its fruit man can live forever.
I love how this page that’s ten years old is current, mathematically speaking.
Thanks for sharing the fascination!
Actually foot in Spanish is pie