Refinding Phi, Part 3.

Continuing on from the end of the last post:-

 
 
 



The Ratio seems to Plateau out around F33/F34.


at  1.618933988749894........
 correction  1.618033988749894
 

 

 

Additional,  7/7/2013:-

 

The known value of Phi, to 50 decimal places is

1.61803 39887 49894 84820 45868 34365 63811 77203 09179 80576…….

Or  1.618 033 988 749 894 848 204 586 8………

We were given, in the  “Kind Advice” of  recent post,   

 ∅³⁶   =  33385281.999 999 970 046 681 049 451 6…….  

(22 decimal places).

The 36^th root of 33385281.999 999 970 046 681 049 451 6

  =  1.618 033 988 749 894 848 204 586 8…..

Which is exactly the known value.

………………………….

1/∅³⁶ = ∅^-36    =  0.000 000 029 953 318 950 548 355 3…..

Adding   ∅³⁶   and  ∅^-36    

=   33 385 281 .999 999 999 999 999 999 999 95 53…..

Which is almost 33 385 282, an integer.

………………………

We were given that Phi⁴ is  6.854 101 966 25………    

 (11 decimal places)

And Phi^-4 is 0.145 898 033 375

Adding them together = 7, an integer.

……………

If we work out, with Scientific Calculator, 

The 4^th root of 6.85410196625  = 1.618 033 988 749 913 5

Then that is possibly the value of ∅ which was used.

 try  Phi⁴ using the known value    =

6.854 101 966 249 684 544 613 759 920 8

(I wonder how different in accuracy the various calculators are

-there might be some rounding off of answers.....)

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