The Golden Ratio

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Gods Fingerprint→ The Fibonacci Sequence - Golden Ratio and The Fractal Nature of Reality

"Fibonacci numbers are of interest to biologists and physicists because they are frequently observed in various natural objects and phenomena. The branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers.

A Sanskrit grammarian, Pingala, is credited with the first mention of the sequence of numbers, sometime between the fifth century B.C. and the second or third century A.D. Since Fibonacci introduced the series to Western civilization, it has had a high profile from time to time. Recently, in The Da Vinci Code , for example, the Fibonacci sequence is part of an important clue."

[Bible Speaks]

A Little Bit About the Golden Ratio    

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WHO DESIGNED THIS?

DID COME ABOUT BY CHANCE?

#OurCreatorJehovahGod?

Think of 2 numbers. Create the third number by adding the first and second numbers, get the fourth buy adding the second and the third number and continue this trend (eg; 1,2,3,5,8,13,21). Once you have 10 numbers or so, find the ratio between the last and the second last number (divide the bigger number by the smaller number) and you should discover that the answer is close to 1.6180339887etc.

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Congratulations! You have just demonstrated to yourself the “Golden Ratio” or Phi Φ which is based on Fibonacci Numbers, where every number in the sequence (after the second) is the sum of the previous 2 numbers. So, what is so special about this number sequence?

(1) Its mathematical properties:

-The golden ratio is the only number whose square can be produced by simply adding 1 and whose reciprocal (1/x) can be produced by subtracting 1.- If you take a golden rectangle; a rectangle whose length to breadth is within the parameters of the golden ratio and cut out a square, you will find that what remains is another, smaller golden rectangle.- The golden ratio, like Pi, is an irrational number; there is no equivalent fraction for Φ and its decimal keeps going and never stops.- Its digits, of which 10 million were computed in 1996, never repeat.

(2) Its presence in nature:

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The Golden Ratio occurs in nature in many forms: sunflowers, pine cones, leaves, mollusks and so on. This is largely because one of the best ways to efficiently pack things tightly together is using the Fibonacci sequence. This is attributed to the fact that the golden ratio is the slowest of all continued fractions to converge. As an example, take the arrangement of leaves on the stem of a plant. As each new leaf grows, it does so at an angle offset from that of the leaf below. The most common angle seen between successive leaves is 137.5 degrees or the golden angle. Why is it called this?? Well, because 360 degrees divided by the golden ration is, yeah you guessed it, 137.5. Cool eh?!

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(3) The golden ratio applied to the arts:

While deliberate, the golden ratio can be seen in some of the most famous and beautiful works of art. Claude Debussy used it overtly in his music (more recently, the band “Tool” have used it in the song Lateralus) and Le Corbusier in his architecture. There are also claims the number was used by Leonardo da Vinci in the painting of the Mona Lisa, by the Greeks in building the Parthenon and by ancient Egyptians in the construction of the Great Pyramid of Khufu.

So, there you go- a few examples of the beauty of maths, or, if you’d prefer; the maths of beauty.

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[Bible Speaks]

Tools’ Lateralus with the golden ratio (definitely worth a watch if you’re a Tool fan): 

 

 

 

More information:

http://www.mathsisfun.com/numbers/golden-ratio.html (Good for kids)

http://www.goldennumber.net/ (For kids and adults alike!)