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Encounters of the KNOWN kind - Reposting from Mystery of the Iniquity website

This postis from a very important and insightful website called “Mystery of the Iniquity”  www.mysteryoftheiniquity.com - I highly recommend it to any of you that earnestly seek the truth within the (so called) mysteries that seem to surround us…. and seeking answers in regards to things of a spiritual nature especially. 

The blog is informative and there is a welcoming exchange between the writer and the visitors to the page that nearly always makes one think much more in depth about these matters!

The Fibonacci Sequence in TOOL's "Lateralus" ~ The Golden Spiral and Sacred Geometry in Music

                     Tool Spiral Sticker

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Also see my “NOTES" on Facebook for all my favorite lyrics by TOOL Maynard James Keenan quotes!    @  Brenda Herring on Facebook


http://toolshed.down.net/links/

                                                   

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Another example of Fibonacci as expressed in popular music is this video of Jeff Buckley's rendition of the song “Halleluiah" - see below:

http://www.youtube.com/embed/y8AWFf7EAc4?

<iframe width=”640” height=”360” src=”http://www.youtube.com/embed/y8AWFf7EAc4?feature=player_embedded” frameborder=”0” allowfullscreen></iframe>

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GOLDEN RATIO

http://www.tokenrock.com/explain-Golden-Ratio-177.html

THE GOLDEN SPIRAL

The Golden Spiral is in abstract mathematics and chaotic nature. It was first discovered by Pythagoras.

image

The spiral can be derived through the golden rectangle; when squared, it leaves a smaller rectangle behind, which has the same golden ratio as the previous rectangle

If you connect these rectangles with a curve, you have formed the golden spiral. 
You can find this shape almost anywhere in nature: the Nautilus Shell, Ram’s horns,the face of a Sunflower, your fingerprints,  and the shape of the Milky Way galaxy. 

Many artists and architects have proportioned their works to approximate the golden ratio, especially in the form of the golden rectangle.

The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.

Leonardo da Vinci’s illustrations of polyhedra in De divina proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings.(  You should check out De divina proportione on wikipedia, you’ll see the proportions of a face. )

It has even inspired some musicians. 
In fact, the song Lateralus by Tool is completely based on the fibonacci Sequence.  The Fibonacci sequence shares a relationship with the Golden spiral, which might be what the ‘spiral’ mentioned several times later in the lyrics is referring to. In fact, the syllables length itself spirals-in and spirals-out on the sequence: ‎1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 8, 5, 3.  Keenan begins singing at 1:37 into the song. 1 minute 37 seconds, or 97 seconds, is approximately 1.618 minutes. This happens to be the Golden ratio, which is also closely related to the Fibonacci sequence.

It is very amazing what they did,  you should check it out. 

(Click to link to song) 

Adolf Zeisingfound the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors.
In these phenomena he saw the golden ratio operating as a universal law.

In 2003, Volkmar Weiss and Harald Weiss analyzed psychometric data and theoretical considerations and concluded that the golden ratio underlies the clock cycle of brain waves.
 
In 2008 this was empirically confirmed by a group of neurobiologists.

In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.

 It is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

( Source/sources: http://en.wikipedia.org/wiki/Golden_ratio ; and possibly some of the sources listed on that wikipedia page.) 

 

 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165l580141,267914296…….

The Fibonacci Number And The Golden Rectangle.

THE FIBONACCI SEQUENCE:

       

Fun With Fibonacci 


The Fibonacci sequence is an extremely well known sequence of numbers, with several interesting properties. The sequence itself, is made by adding the most recent two numbers together to find the next one. However, as you may have inferred, you need two numbers to start with. The sequence starts with 0,1. If continued, it comes out as: 0,1,1,2,3,5,8,13…

Interestingly, the ratio between the numbers is virtually the same as the golden ratio. This ratio is symbolized by the Greek letter  φ, pronounced “phi.” The golden ratio is said to have an aesthetically pleasing effect when applied to the sides of a rectangle (with a unit of 1, the ratio would be 1:1.618). These rectangles are said to appear commonly in nature, and are used in many famous buildings, such as the parthenon (picture shown above). Because of their ratio, these rectangles are called golden rectangles. 

An interesting property of golden rectangles is that, when cut into a square and a rectangle, the new rectangle has the same side ratio as the original.

Another cool property of the Fibonacci sequence, is that you can use it to convert miles into kilometers, and vice-versa, quite accurately. This is because the ratio between the numbers in the sequence, and the ratio between kilometers and miles is quite similar. Suppose you want to know how many miles 13 kilometers is. Because the number before 13 in the sequence is 8, you would know that 13 kilometers is about 8 miles. If you wanted to know the conversion of a number that is not in the sequence, you would use multiples of that number. ex. for 10, you would use two 5’.

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You can find a never-ending list of resources on the internet about this subject, especially on YouTube.com — I hope you will become as fascinated as I am about it and do some research!

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