## Phi for “Neo-Phi-tes:”

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 sub-atomic 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?

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

Kinson says

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.

Greg says

“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 “$”.

winnie says

Joe, really nice. Got lost at a point though.

ferfo says

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 …

Andrea says

Cant Understand Joe…..! Can anyone EXPLAIN….!

Richard Warren says

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!

Peter Hedding says

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.

larry coleman says

“PHI” UNIFIES ALL THING AND SUFFUSES ALL THINGS

Gayatri says

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

Bucky says

I thought Phi is only one Mathematics constant.

I can’t believe it is associated with so many interesting things!

Thanks for your share.

Gregory Weigle says

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.

Nishant Kapoor says

thanks didn’t know that…phi….is associated with so many things

Theo says

PHI is the universal number for All life.

Gary Meisner says

“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.”

'the da vinci code'brought me here. says

totally fascinated!!!!

lammii says

same here

Jim says

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.

Kaleb says

nice!

Jason says

True Dimensions of The Great Pyramid of Khufu… Base=777.03 ft, Height=480.24 ft… Calculated through Phi=1.618

Alex says

Is it true that PHI is Gods building block.?

Noor Zahra says

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

Gary Meisner says

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.

Albino Giraffe says

This mind-blew me so good. I love the orgasmic effect it instigates in my mind. Truly a large phenomena, and will always be on my mind

jim carlin says

I read-the male brain is a line

the female brain is a wave

viva la difference

which is language of the heart

Lakrtzmth says

Phi is amazing.But nobody in my year knows what it is.I’m 10.

Peter Hedding says

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 Self-Realization 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 Self-Realization 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.

Robert elvis Barkley says

Very intriguing. I appreciate you sharing

Nami says

The ‘Da Vinci Code’ does wonders!!! Thank you @jonathan, it helped a lot!!

jim carlin says

Occam’s razor=be brief

over lapping ellipses=symbol for empathy

there is a good orderly direction=a safe universe

Leo Darnell says

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.

Andrea says

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.

Andrea says

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.

Erik Swain says

Pi is not phi……

Cal Johnson says

awesome!!! 67 years old and learning things everyday. PHI is new and exciting for me.

j carlin says

kewl-numbers

jim carlin says

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:)

Sue says

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.

Gary B Meisner says

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 http://www.goldennumber.net/category/cosmology/.