轟(to-do-ro-ki) Season 6 Mini-Appendix 3 ～ Please help me find friends of the Golden Ratio! Part 2

60stars astrology

English version

By Tokyo-Tanuki

60stars Astrology Season 6

 

轟（to-do-ro-ki)  Season 6 Mini-Appendix 3

Please help me find friends of the Golden Ratio!　Part 2

1. In the previous article, I wrote,

☈ = (1+√13)/2 = 2.302775637731....　

Then,
☈×4=9.211102550...　
☈squared = 5.302775637731.... = ☈+3
☈cubed = ☈ squared + 3☈ = 4☈ + 3 = 12.211102550...
☈6th power = (☈ x 40) + 57 = 40☈ + 57 = 149.11102550...
and so on.

And if we do further calculations,

☈ 4th power = ☈ squared + 6☈ + 9 = 7☈ + 12 = 28.11942946412...

☈ 5th power = ☈ x (☈ fourth power) = 7☈ squared + 12☈ = 19☈ + 21 = 64.75273711690...

☈ 6th power = ☈ x (☈ fifth power) = 19☈ squared + 21☈ = 40☈ + 57 = 149.11102550..

☈ 7th power = ☈×(☈ sixth power) = 40☈ squared + 57☈ = 97☈ + 120 = 343.3692368600...

...the result is as above. 

These can be calculated more and more from the basic formula, " ☈squared = 5.302775637731.... = ☈+3" .

But later and later we no longer see the sequence of numbers 

“02775637731...”and “11102550...”.

2. On the other hand, if you calculate various additions, subtractions, and divisions about "☈",you get as follows;

☈ cubed - 3 = 12.211102550 - 3 = 9.211102550.... = (☈ sixth power - 57)/10 = 4☈.
(☈+1) cubed = 36.02775637731.... = 10 (☈+1) + 3
(☈-1) cubed = 2.211102550297.... = ☈ cubed - 10 = 4☈ - 7
(☈+1) x 4 = 4☈+4 = ☈ cubed + 1 = 13.211102550297....

Then, looking at the smaller numbers,
1/(☈-2) = ☈+1 = 3.302775637731....
4/(☈-2) = ☈ cubed + 1 = 13.211102550297....
3/☈ = 1.302775637731....

...Hmmm, here, “02775637731..” “11102550..” are everywhere, all in places.

...But still I'm not clear if we can say that √13 is even as fancy as Φ.



3.  By the way, 
How about the other case, for example the case of "√17" ?
So, let us consider the case of { (1+√17) / 2 }.

{ (1+√17) / 2 } = 5.123105625617.... /2 = 2.561552812808.... ＝☂(RAIN).

Then,

☂ squared = 6.561552812808.... = ☂ + 4, and the fractions are equal.

But rather,
☂ x 2 = 1 + √17 = “5.123105625617....” = (2☂) = ❆ (SNOW),
It is more interesting to use this ❆ as a basis.

In this case, 
❆ squared = 26.24621125123...

❆ cubed = 134.4621125123.... 

“4621125123....”  the sequence of numbers appears in the square and in the cube.

Furthermore, 2×❆ = 2❆ = 10.24621125123...

Therefore,

❆ squared = 2❆ + 16 = ❆ + 21
❆ cubed = 20❆ + 32 = ❆ + 129

(10×❆ squared)-128 = (20❆ + 160)-128 = ❆ cubed
(10×❆ squared) = ❆ cubed + (2 to the 7th power)

Also, for smaller numbers,

1/{❆+3} = 0.123105625617.... = ❆-5

1/{❆-5} = 8.123105625617.... = ❆+3


Well, it's a bit more complicated than in √13' s case, but √17' s case is also somewhat similar with √13' s case.

🌟　🌟　🌟　🌟

4. The fractions of Φ are all together in 1/Φ, Φ and ΦΦ, i.e., minus 1st power of Φ, plus 1st power of Φ, and Φ squared have the same fractions.

It feels very special !

..Then, when a = 3, that is in the case of ☈ =｛ (1 + √13) / 2｝, even if the fractions are together in the 3rd and 6th power,　are these phenomena more common than I thought ?

...With these questions, I will continue with the next (final) article.




Tanu-chan💓  TOKYO-TANUKI💛