The Divine Proportion
I've been reading the Dan Brown novel "The Da Vinci Code" and it mentioned a mathematical phenomenon know as the Devine Proportion or the Golden Number. The number is commonly called phi (pronounced 'fi' as in 'fly' and is not to be confused with pi) That number being:
1.6180339887...
Now, before you start thinking that I've completely lost my mind I'm actually going somewhere with this. The reason I'm so intrigued by this seemingly irrelevant number is that it seems to be, well, divine.
Just as pi 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.
What makes phi even more unusual is that it can be derived in many ways and shows up in relationships throughout the universe. I will give you a few examples that will flip your mind..
No doubt everyone still reading this post (I admit, I’m going to lose a few of you by this point) will have see the Fibonacci series:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
Where each new number in the series is simply the sum of the two before it. Simple enough. Now, the ratio of each successive pair of numbers in the series approximates phi, as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60.
We see the ratios of the successive numbers in the Fibonacci series quickly converge on Phi. After the 40th number in the series, the ratio is accurate to 15 decimal places.
Is this mathematical equation merely a coincidence? Many doubt it (thus attributing the phenomenon to some other Devine inspiration). Virtually everything in nature is structured around this number. Examples:
Music:
The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as:
There are 13 notes in the span of any note through its octave.
A scale is comprised of 8 notes, of which the
5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is
2 steps from the root tone, that is the
1st note of the scale.
Note too how the piano keyboard scale of C to C above of 13 keys has 8 white keys and 5 black keys, split into groups of 3 and 2.
Ever wondered how Beethoven managed to write great musical pieces such as Fur Elise, despite being deaf??? Here's your answer.. Beethoven was a mathematician (Personally, I've always know this but could never figure out how he actually related it to maths)
I guarantee you that even our most favourite Tiesto tracks are structured in similar ways.
The Human Body and Nature:
Take out a tape measure and find out exactly how tall you are from head to toe. Now find the vertical distance from the ground to your belly button. What's the ratio between the two numbers? 1.618...
Measure the length of your arm from shoulder to fingertips. Now measure the distance from your elbow joint to your fingertips. The ratio? 1.618...
Measure the length of your leg, from hip to the ground. Now measure the length from your knee to the ground. Again.. a ratio of 1.618..
The vertical length of your head is 1.618 times the horizontal width of your head.. Here's a nice picture of George Clooney to show my point:
The middle range of typical body temperatures of mammals (including animals other than humans) is about 38.1 or 38.2 degrees C. Notice anything?? Lets remember that your bodies are made up comprising of mostly water and the boiling temperature of water is 100 degrees. The difference between the two numbers? 61.8. The Devine proportion still involves itself.
The human heartbeat (according to an ECG machine):
A healthy and harmonious heartbeat is said to follow the properties of phi. That is the ratio between the QRS complex and the T wave is proportionately related to phi.
Now, if any of you actually take a tape measure out you might find some variance. That's to be expected. But what is noted is that beauty (yes, beauty) is measured according to this number. The closer your physical structure is to phi, generally the more beautiful and proportionate you will seem. This extends between cultural and racial boundaries.
Not only animals and other living organisms follow phi, but also structures of the rings of the planet Saturn (RE: The Cassini division in the rings of Saturn falls at the Golden Section of the width of the ring.)
Venus orbits the Sun in 224.695 days while Earth orbits the Sun in 365.242 days, creating a ratio of 8/13 (both Fibonacci numbers) or 0.615 (close enough to phi.)
Stock Market Trends and the Fibonacci Series:
Changes in stock prices largely reflect human opinions, valuations and expectations. A study by mathematical psychologist Vladimir Lefebvre demonstrated that humans exhibit positive and negative evaluations of the opinions they hold in a ratio that approaches phi, with 61.8% positive and 38.2% negative.
Architecture & Art:
Leonardo Da Vinci, along with many other great artists, used this principles of phi to paint their masterpieces. Look at the Last Supper:
It was even used as a principle to build the Great Pyramids in Egypt:
Finally, Theology/Religion:
In Exodus 25:10, God commands Moses to build the Ark of the Covenant, in which to hold His Covenant with the Israelites, the Ten Commandments, saying,
"Have them make a chest of acacia wood-
two and a half cubits long,
a cubit and a half wide,
and a cubit and a half high."
The ratio of 2.5 to 1.5 is 1.666..., which is as close to phi as you can come with such simple numbers and is certainly not visibly different to the eye. The Ark of the Covenant is thus constructed using the Divine Proportion. This ratio is also the same as 5 to 3, numbers from the Fibonacci series.
In Genesis 6:15, God commands Noah to build an ark saying,
"And this is the fashion which thou shalt make it of: The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits."
Thus the end of the ark, at 50 by 30 cubits, is also in the ratio of 5 to 3, or 1.666..., again a close approximation of phi not visibly different to the naked eye. Noah's ark was built in the same proportion as ten arks of the covenant placed side by side.
And the coolest part of it (according to me) The Number 666 is related to Phi:
Revelation 13:18 says the following:
"This calls for wisdom. If anyone has insight, let him calculate the number of the beast, for it is a man's number. His number is 666."
This beast, regarded by some as the Anti-Christ described by John, is thus related to the number 666, one of the greatest mysteries of the Bible. Curiously enough, if you take the sine of 666º, you get -0.80901699, which is one-half of negative phi, or perhaps what one might call the "anti-phi."
The trigonometric relationship of sin 666º to phi is based on an isosceles triangle with a base of phi and sides of 1. When this triangle is enclosed in a circle with a radius of 1, we see that the lower line, which has an angle of 306º on the first rotation and 666º on the second rotation, has a sine equal to one-half negative phi.
In this we see the unity of phi divided into positive and negative, analogous perhaps to light and darkness or good and evil. Could this "sine" be a "sign" as well?
In addition, 666 degrees is 54 degrees short of the complete second circle and when dividing the 360 degrees of a circle by 54 degrees you get 6.66... The other side of a 54 degree angle in a right angle is 36 degrees and 36 divided by 54 is .666.
The teachings of most religions express the thought that part of God is within each of us and that we are created in His image. The pervasive appearance of phi throughout life and the universe is believed by some to be the signature of God, a universal constant of design used to assure the beauty and unity of His creation.
My Question:
What is your interpretation of the Divine Proportion... Is it coincidence... Is it merely nature’s equilibrium... Is it, in fact, the signature of God..?
Nonetheless, it is a pretty cool number..
___________________
A witty saying proves nothing.
-Voltaire
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