巛（ka-wa) Season 6 mini-appendix ３ “ Meet the friend of Φ!, Maybe ? ? ”

60stars astrology

English version

By Tokyo-Tanuki

60stars Astrology Season 6

巛（ka-wa) Season 6 mini-appendix 3

 “ Meet the friend of Φ!  Maybe! ? ? ”

1.  Well, at the end of the year, I tried to find a friend of the golden ratio Φ, but it didn't quite work out.

So, today, I would like to introduce to you a baby that might be a friend of this one.


It is {(√7 + √3)squared}/2 squared.

At first I didn't think it could be a Φ’ｓ friend.

Why this number? 

Because,

Φ is (√5 + 1)/2, though,

In this case, 1, 2, and 5 are used among the prime numbers.

And Φ is fancy, isn't it?

It is related to the pyramids a lot, and Leonardo da Vinci used it a lot, too!


But of the prime numbers, 3 and 7 are a bit neglected.
They don't get much of a chance to play an active role, or so ....

So I was looking for the advantages of these babies.

And to my surprise, I found that they may be friends of Φ.


2.　 '{(√7 + √3)squared}/2 squared"  is a bit too long.

So, I thought of a name for it, but I couldn't find a good one.

So, let's call it "N" from the end "n" of the names of Mr. Ramanujan and Mr. Perelman, both of who I respect very much.


In other words, N = {(√7 + √3)squared}/2 squared = 4.7912878.......... 

So.If we calculate, N squared = 22.95643923.......... and then,
N-squared = 5N-1.

Well, so far, it is quite normal.

However, this "N" may have a property similar to Φ.
 First,
(1) It must be spiral 🌀, i.e., it must go on forever.

Φ is
Φ × Φ × Φ × Φ × Φ × ......... 
= ●●.999999999999.........
or
＝●●.000000000000.........

and the more you multiply Φ by Φ or the more the number, 

the longer the decimal point 99999999999999999.........or　●●.000000000000.........also becomes longer. 

However, it will never be zero.

"N", for example,
N×N×N×N......... N = ●●.9999999999999......... 

This also never becomes zero.

For example,
N to the 10th power = 6375622.999999998431.........
And,
N to the 100th power is, 110975289524608132128497082362575073638552505717848036754903981578127.999999999999999999999999999999999999999999999999999999999999999999990.........
 
....like this!


(2)  I wrote about this earlier in an article called Between Φ and 1/Φ, no matter how many times Φ is squared, if we subtract a constant number a (1.118033988.... = √5/2), we end up with a simple and clean number.

For example,

The fourth power of Φ is 6.85410......... but if we keep subtracting 1.1180333988......... 

Then, by subtracting
Φ squared -1.118033988........ -1.118033988......... -1.118033988 = 3.5.


For N, for example,
N cubed = 109.9909083......... 

But if we subtract N itself from this number again and again, we get
N cubed - N - N - N - N - N ......... = N cubed - N x 24 = -5

For the fourth power of N, subtract N x 115, and for the fifth power of N, subtract N x 551, and try it out!


......... Again, N is just like Φ.



(3) Now, the most important thing is "Coolness".

For Φ,

Φ to the minus one power = 0.618033988.........
Φ = 1.618033988.........
Φ squared = Φ + 1 = 2.618033988.........

which is a cool visual like, as the multiplier increases, it increases by 1.


Then, in the case of N, it's like,
(N+1)squared/N = 7
(N−1) squared/N = 3

And,

(N )squared / N = N,

(N-1) squared : N squared : (N+1) squared　
= 3 : N  :7

......... It's not that bad visually between lucky numbers!



Although maybe not as good as Φ,
from three points: 🌀, the relationship between powers and multiples, and visuals,

This "N" = {(√7 + √3) squared}/2 squared = 4.7912878..........as a friend of Φ, maybe! 

Tanu-chan introduces it to everyone!

....Now, then, what exactly can we use this "N" for? 

Mmm......... I will think about it, so please just give me a moment !

4. 　By the way, with a decimal point, 999999......... and 00000000.... are not only the case of Φ or "N".

For example, in the case of (√11 + √13)/2, the decimal point is actually also followed by 999999.......

Try running this through the calculator just for a second.

If you think, “It doesn't come out,” look at the decimal point all the time! 

For example,
(√11 + √13)/2 to the even power, for example, to the 1000th power,
....9999999......... continues from 500 to 840 digits after the decimal point.


If you power it by 7500,
.....9999......... continues from about 3750 to 6300 decimal places.

 
Then after that, it returns to a random number.


Why ....9999..... in halfway?
I'm not quite sure why.


Well, so there are quite a few things that can be 🌀 if you look for them, but mainly from a visual point of view (coolness), I think,

N = {(√7 + √3)squared}/2 squared = 4.7912878.......... 

may be considered to be a friend of Φ!


......but I feel Φ has much more closer friends.....

Maybe we can find them later!

🌟　🌟　🌟　🌟

Well. 

Of course, I'm not sure what that means mathematically 💕.

So, just have fun!

That's all for today



Tanu-chan💓 　TOKYO-TANUKI💛