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[MarkE]

There you go again. One can generate a Fibonacci sequence with any starting number, string it out to sufficiently large numbers, and arrive at Phi by taking the ratio of the last two numbers in the sequence.

4,4,8,12,32,52,84,136,220,356,576,932,1508...
1508/932=1.618025751...

The further out you extend any Fibonacci sequence, the closer you get to Phi when you take the ratio of the largest two numbers in your sequence.

And you didn't know that, O Great Genius? Or maybe you did, but you just wanted to misrepresent the Truth once again in a weak attempt to bolster your gobbledegook "explanations".

The relationships in the golden ratio are:  X/Y = Y/(X+Y).   For sequential Fibonacci sequence values:

X_n+1 = X_n + X_n-1

So, the ratio:  X_n/X_n+1 = X_n/((X_n + X_n-1)

And if the ratio of two sequential Fibonacci numbers equals phi then:

X_n/X_n+1 = X_n+1/(X_n+X_n+1)

And therefore:

X_n/((X_n + X_n-1) = X_n+1/(X_n+X_n+1)

Consequently, if the ratio of any two successive Fibonacci numbers is phi, then the ratio of all successive Fibonacci numbers is also exactly phi.  But it only works if first the ratio of a pair does equal phi. 

[MarkE]

8/13 = 0.615384615

I had to do a double take on that graphic.  How could someone claim with a straight face that:  8/13 = 13/21  13² = 169.  8 * 21 = 168  So they differ by 1/273.  Similarly for 13/21 and 21/34, 442 <> 441.  But 1/714 sure is less than 1/273.

13/21 = 0.619047619

21/34 = 0.617647059

So  much for your plagiarized little drawing's "EQUAL" statements.

Maybe some inequalities are more equal than others.

[synchro1]

Horn:

[TheoriaApophasis]

But it only works if first the ratio of a pair does equal phi.

thats where you and most others dont get it, per se.   

1, and 1, are still the ratio of 1 to Phi,  since 1 is to Phi as Phi is to 1.    Or precisely, 1 is Phi , and Phi is 1, ( likewise phi, 1/Phi, Phi^-2, ^-3, squared and cubed)


The Greek Platonists discovered this fact 2800 years ago
likely the Pythagoreans before them.

The entire arena of Incommensurability is beyond the kin of absolutists 

or in greek  Aoristos   (as implied the aoristos dyas, or ancient Egyptian  Ahorizoma)    A+horizon (anti-horizonal, or incommensurate)
I discovered that secret in Plato's Republic 509d-511 on the "divided line"

But thats too abstruse to discuss in this room full of literalistic materialists. 
But its ok, thats called literalistic anti-intuitivism.


I did a very "painful" translation from the ancient Greek of all occurrences of Incommensurability passages of Plotinus.
https://archive.org/details/IndefiniteDyadPlotinusMetaphysicsMysticism



Ultimately, all literalistic minds COUNT BEANS 

10 beans, / 2 = 5 beans.



Ultimately, they "MISS" that its all just a BEAN, 1 bean, and 1 bean ONLY.    Many or few, divided or Undivided...

still just one goddamn BEAN   

[Pirate88179]

thats where you and most others dont get it, per se.   

1, and 1, are still the ratio of 1 to Phi,  since 1 is to Phi as Phi is to 1.    Or precisely, 1 is Phi , and Phi is 1, ( likewise phi, 1/Phi, Phi^-2, ^-3, squared and cubed)


The Greek Platonists discovered this fact 2800 years ago
likely the Pythagoreans before them.

The entire arena of Incommensurability is beyond the kin of absolutists 

or in greek  Aoristos   (as implied the aoristos dyas, or ancient Egyptian  Ahorizoma)    A+horizon (anti-horizonal, or incommensurate)
I discovered that secret in Plato's Republic 509d-511 on the "divided line"

But thats too abstruse to discuss in this room full of literalistic materialists. 
But its ok, thats called literalistic anti-intuitivism.


I did a very "painful" translation from the ancient Greek of all occurrences of Incommensurability passages of Plotinus.
https://archive.org/details/IndefiniteDyadPlotinusMetaphysicsMysticism



Ultimately, all literalistic minds COUNT BEANS 

10 beans, / 2 = 5 beans.



Ultimately, they "MISS" that its all just a BEAN, 1 bean, and 1 bean ONLY.    Many or few, divided or Undivided...

still just one goddamn BEAN   

I am no math wiz but this seems like you are saying that if you multiply a number by 2, then that result can always be divided by 2.
Seems like a circular argument to me...but, as I said, math is way down the list of things I am good at. (Way, way down)

Bill