I. Theory: Mathematics of PI (Pie) Day, Circle
II. Mathematics of Divine Proportion, Golden Number PHI, Golden Proportion
III. Relation between Divine Proportion and Fibonacci Numbers
IV. Divine Proportion, Golden Ratio, Golden Number and Real Life
V. Historic Beginning of PI Day: American Revolution
Authored on 3.14 00:00:00 2002; latest update 3.14.15.
First capture by the WayBack Machine (web.archive.org) on April 20, 2002.
Specific to the American civilization, the date is expressed as 213, instead of the international method of 123 (ascending order: day - > month - > year). March 14 is expressed as 314, therefore 3.14, therefore the inception of the number PI. PI is the divine number that no human can ever calculate precisely (except for a numerical system with PI as its base). It is at the heart of divine circle. “The area of the circle is equal to PI times Radius square.”
PI is the result of dividing the circumference (perimeter) of the circle (L) by its diameter (D). The great Greek mathematician Archimedes was the first to calculate PI. He approximated PI to 3.14, a value still in wide use today (in the decimal system).
"Why so - month - > day - > year?" terrestrials everywhere wonder.
I am fortunate to have learnt recently a very tight secret. It was passed on to me from a scholar who desired to remain unidentified. The scholar has also remained outside the Internet revolution, unable to write HTML files and author websites. My Web site is the reason she decided to share with me the tightest secret in human civilization. In turn, I promised to make public extraordinary information via the Internet, on my Web site.
When the most precise atomic clock beams exactly 00:00:00 3.14, Almighty Number visits with the President of the United States. The President himself bakes a large apple pie. Procuring the ingredients is an extraordinary opération d'état. It is code named Newton's Pie. Almighty Number cuts it into the perfect circle. Then, Its Almighty slices it into portions precisely calculated by the Golden Number or Divine Proportion.
Almighty Number always gets to eat the 61.8% slice. Even though represents only 38.2% of the divine pie, the presidential slice is quite impressive by human standards. Not all Presidents have been able to eat entirely the presidential slices of the pie. Legend has it that skinny Abe Lincoln would have gained reasonable weight, had he eaten to the last bite his presidential slices of the Newtonian pie.
Let's take a segment and divide it into two parts, a and b. There are two conditions that lead to the Golden proportion:
1) b greater than a (b > a);
2) a/b = b/(a+b).
(The Ancients, by the way, expressed the Divine Proportion in mystical chants comprehensible only to highly initiated cult members. “I am the mean and the extreme!”, they were chanting.)
If we make a + b = 1, the relation a/b = b/(a+b) leads to the well-known equation:
Let's apply the quadratic formula to get the two roots known as the golden number (or that kind of idiotic label of ”divine” proportion):
|−b ± √ b2 - 4ac|
The two roots of the equation are known as The Golden Number or PHI:
Normally, if big / small then Φ = 1.618
if small / big then Φ = 0.618
(Side bar: In the English speaking nations, some write it as Go(l)d(en), indicating the Golden Number as the manifestation of God.)
The most mind-boggling expression of the Golden Number is an infinite series of 1, in the form:
(Φ = 1 plus (1 over (1 + (1 over) (1 + 1 over))))… and so one to infinity. It looks more like a stairway all the way down to minus infinite. The initiated say it is the stairway Almighty Number takes to descend to the earth.
Many people are familiar with a string of numbers such as this one: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The Nth term of the Fibonacci series is constructed as the sum of the two preceding terms; e.g. 55 = 21 + 34. The term #10 = the term #8 + the term #9.
There is a natural correlation between the Fibonacci numbers and the divine proportion, or the golden number PHI. The ratio between two consecutive numbers in the Fibonacci Series tends to the Golden Number Φ: 0.618… or 1.618… As in the example above:
Fibonacci #9 / Fibonacci #10 = 34 / 55 = 0.61818…
Fibonacci #10 / Fibonacci #9 = 55 / 34 = 1.61764…
Any three Fibonacci numbers a, b, c satisfy the relation c = a + b. Thus, the ratio b /(a + b) tends to the golden ratio or golden number. The longer the Fibonacci series, the closer the ratio of two consecutive terms to the golden number PHI.
I wrote a program to generate Fibonacci numbers and to calculate the golden ratio: Fibonacci. You can download it from my free downloads site. The software is freeware. One need not be a … golden child in order to run Fibonacci.EXE! The Fibonacci numbers grow very big after 50 terms or so. Try first the defaults: up to 1000 terms and screen display. Read a more detailed analysis:
It also brought to life a divine audio masterpiece: Led Zeppelin's Stairway to Heaven. The musical mystics “think” that the distance between the notes of Stairway to Heaven can be represented by the PHI golden number. Did you know that one radio station in Florida plays Stairway to Heaven over and over, the New Year's Eve? They do not play any other song, December 31 until New Year's Day, January 1, 00:00:01. Humans get addicted especially to the divine…
I must make this confession here. I was preoccupied with the divine proportion in my pre-philosophical past. I wrote my first and only novel (never to be published!) following strictly the requirements of the golden proportion. The number of words per line over the number of lines per page had to be compatible with the golden number ratio. The number of lines per page over the number of pages in the book had to lead to the divine proportion. I still have the manuscript here. I never read the story more than once. I only take measurement of the divine proportion parameters sometimes.
A beloved lover of the opposite even measured our parts and she did come up with the precise golden proportion. The measurements made me lose consciousness one day. "We are sentenced to immortality," she warned me. She and I abruptly went different ways; we never, ever, said good-bye to each other. We may believe we'll see each other again on the stairway to heaven.
She and I had many secret names, code names of sorts. We even invented a secret alphabet. We had used first the Greek alphabet in our native tongue mixed with some French and English. Many people figured out the alphabet easily. She named me Caravaggio, while I called her Caravaggia. The feminine, you know. We were not violent like the painter who is the most human philosophical artist of all time. Say human, say sinner, but don't hide the sins. Caravaggia and I are just unconventional. We hate convention, because defies a fundamental Universal law: Change. And things change following the Divine Proportion. Beautiful sometimes, horribly sometimes — depends on the Perspective.
"You shall always worship Me and only Me”, Almighty Number thundered. “You shall build a world upon my laws, and formulae, and equations! And you shall always celebrate Me every year, at this very moment!"
There are many hints of that memorable event. Look at the seals of the US government. They are the representation of the perfect circle! The first flag of the United States represented a circle of stars! The thirteen stars represented Almighty Number and Its Twelve Hours.
There are no religious symbols in the government of the United States. Doesn't that fact alone raise serious questions? How was that possible, in a strongly religious (Christian) society, in an era when religion even decided life or death? The symbol of the cross is nowhere to be found in the armory of the United States! It is said that Almighty Number ordered in a lightening manner: “You shall not use my operational symbols as symbols of your passing power! For the cross resembles +, my symbol of addition. For I add and I take randomly, but you can't and shall not!”
The Confederate States used the “X” symbol during the Civil War. “I shall punish them with a vengeance! For X is my reserved operational symbol of multiplication. For I multiply and divide as I randomly please, but you shall not!” One reason the division of the United States was so cruelly stopped: The X on the Confederate flag.
Well, yes, there is also the circular shape of the nuclear explosion…
• Scientia is the collection of the most important programs in software category 5.6: The best scientific software for mathematics, probability, statistics, combinatorics, lexicographic ordering. Only registered members may download my software. Once downloaded, the software is free to run for… an eternity… if The Divine Proportion allows!
I wish to each and every one of you a happy PI Day — male and female, leftist and rightist, sinner and saint, friend and foe! May Almighty Randomness grant us always the divine proportion between our hopes and our endeavors! And thus we shall not count things we lapse and discount blessings we touch.
Read Ion Saliu's first book in print: Probability Theory, Live!
~ Discover profound philosophical implications of the Formula of TheEverything, including the important numbers Divine Proportion, Golden Number PHI, PI.
For the English speakers who search the Internet on the pronunciation of PI, PHI, Fibonacci, da Vinci:
The Greek symbol φ or Φ PHI is pronounced like Fee.
The Greek symbol π or Π PI is pronounced like Pea.
Fibonacci is pronounced like Fee-boh-NAH-chee.
da Vinci is pronounced like dah VIN-chee.
More interesting mathematics: