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[TinselKoala]

Sorry son,  reciprocal VALUES of PHI can only be generated using 1, 1, 2, 3, 5, 8...........


said values being :

1/Phi^-3    (.23606)

1/Phi^-2   (.3819..)

1/Phi  (.618033)

Phi squared

Phi cubed  (4.23606....)




L O S E R 

Wrong again! Do the math. ANY Fibonacci sequence generates an increasingly accurate APPROXIMATION of the irrational number PHI, the Golden Section, and these approximations behave just as your favorite APPROXIMATION does.

Or can you even do the math? Apparently not, since you think that 8/13 = 13/21 = 21/34.

[TinselKoala]

Contextualize  IRRATIONAL moron......       The Greek Platonists, Italians, and leonardo da vinci  said Phi was:::


"the most rational and beutiful of ratios"



Idiot moron, PHI is a RATIO........... not a number !!!!!!!!!!!!   


You must be drunk!!!!!   




All of nature is "painted" in the golden RATIO (a ratio, drunk, not a number!!)

Call it whatever you like. It is an IRRATIONAL number, a RATIO that cannot be exactly specified by a RATIO of integers.  You can't get away from the truth here by redefining things. If it's a RATIO, why do you keep expressing it as "1.618..." ? That's a representation of a NUMBER, an IRRATIONAL one at that.

[TheoriaApophasis]

ANY Fibonacci sequence generates an increasingly accurate APPROXIMATION of the irrational number PHI,

Sorry, son.    It begins with 1



what number moron?    Its a RATIO   



Or didnt you know that "Phi is to 1, as 1 is to Phi" 



Drinking the strong stuff today are ya? 

[TinselKoala]

http://www.goldennumber.net/what-is-phi/

The golden ratio also is called the golden mean or golden section (Latin: sectio aurea).^[1][2][3] Other names include extreme and mean ratio,^[4] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,^[5] and golden number.

http://en.wikipedia.org/wiki/Golden_ratio

When you write it as 1.618.... it is a NUMBER. When you write it as, say, 1974/1220, it is a RATIO. You cannot however exactly specify it by a RATIO of any two integers, you can only APPROXIMATE it... that is why it is called an IRRATIONAL NUMBER.

[TheoriaApophasis]

If it's a RATIO, why do you keep expressing it as "1.618..." ? That's a representation of a NUMBER, an IRRATIONAL one at that.

So mother nature is irrational?     Do tell.



Its a ratio of 1 (the given) to Phi (1.618033......)....


... the only natural progression of which is 1, 1, 2, 3,5, 8.......


anyone on here can GOOGLE "Golden ratio sequence" and see that for themselves son.



Sequences APPROACHING PHI (1.618033), is not a logarithmic natural progression which ARRIVES at the SHORTEST SEQUENCE ending in the RATIO of  1 to PHI


* Derp   




ALSO, dumbass, none of your sequences can produce the golden Angle ,   137.5077   (or 137.5 degrees)