Golden Spiral and Fibonacci: Difference between pages

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[[File:FakeRealLogSpiral.svg.png|thumb|Approximate and true golden spirals: the green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a golden spiral, a special type of logarithmic spiral. Overlapping portions appear yellow. The length of the side of a larger square to the next smaller square is in the golden ratio.]]
[[File:360px-Fibonacci spiral 34.svg.png|thumb|The Fibonacci spiral: an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling;this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.]]
In geometry, a [[Golden Spiral]] is a logarithmic spiral whose growth factor is φ, the [[Golden Ratio]]. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.<ref>[https://en.wikipedia.org/wiki/Golden_spiral Golden SPiral]</ref>
In mathematics, the [[Fibonacci]] numbers or Fibonacci sequence are the numbers in the following integer sequence: 1,1,2,3,5,8,13,21,34,55,89,144...


==Approximations of the golden spiral==
If we sum the squares of any series of [[Fibonacci]] numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number.  This property results in the Fibonacci spiral, based on the following progression and properties of the Fibonacci series.The Fibonacci spiral gets closer and closer to a Golden Spiral as it increases in size because of the ratio of each number in the Fibonacci series to the one before it converges on [[Phi]], 1.618, as the series progresses. Beginning with Zero, then 1, it then moves on to the next number, as such :  0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8 and so forth.
'''There are several similar spirals that approximate, but do not exactly equal, a golden spiral. These are often confused with the golden spiral.'''


For example, a golden spiral can be approximated by first starting with a rectangle for which the ratio between its length and width is the [[Golden Ratio]]. This rectangle can then be partitioned into a square and a similar rectangle and the rectangle can then be split in the same way. After continuing this process for an arbitrary amount of steps, the result will be an almost complete partitioning of the rectangle into squares. The corners of these squares can be connected by quarter-circles. The result, though not a true logarithmic spiral, approximates a golden spiral.
When we apply this mathematical formula to quantify or measure the movement of energy or [[Consciousness]] within time or space, the [[Fibonacci]] Spiral loses its connection going back to the Zero point or Source, instead the sequence uses the previous number to add into itself to get to the next higher number of the sequence. The Fibonacci Spiral illustrates the math used to perpetuate the war over energy, therefore the consciousness suppression on the earth, through as when the sequence grows in number or size, it is due to the consumption of the previous values in order to grow itself larger. (See [[Consumptive Modeling]]). Therefore this model is one of [[Metatronic Reversal]] in the consciousness fields that manifests [[Miasma]] fields of the [[Qlippoth]] or Adverse [[Sephiroth]], the [[Phantom Matrix]] in the Tree of life.  


Another approximation is a [[Fibonacci]] spiral, which is constructed similarly to the above method except that you start with a rectangle partitioned into 2 squares and then in each step add to the rectangle's longest side a square of the same length. Since the ratio between consecutive [[Fibonacci]] numbers approaches the [[Golden Ratio]] as the [[Fibonacci]] numbers approach infinity, so too does this spiral get more similar to the previous approximation the more squares are added.


==HGS Reference==


Correct Calculus, Mathematical Code,  Page 80
 
progressively moving out of a Krystic or Divine Template as it Expands.
 
 
 
 
 
==References==
 


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