Φ⁶　60stars Astrology Season Essay　Φ⁶　 "The Crack"

60stars Astrology Season Essay

Φ⁶　60stars Astrology Season Essay　

Φ⁶　 "The Crack"

1．Now, shifting perspective, let us not only vary "P", "Q", "R",

but also the exponents "m" and "n".

Here, let P, Q, R, m, n be integers from −3 to 3.

The simplest case is m, n=0:
±Q(X⁰) ± R(1/X⁰) = ±P

Then ±P becomes (±Q ± R), and solution X can be any number.

At this time, the crack in the world mentioned earlier appears slightly.

2. ....Anyway, trying numbers for n and m,
solutions like 0, ±1, ±2, ±1/2 occur often.

Soon Φ and its reciprocal appear too!

And continuing to substitute numbers into P, Q, R, m, n,
the crack problem arises clearly.

For example, in the simple form:
Xᵐ − 1/Xⁿ = 1

That is: X^(m+n) − 1 = Xⁿ

So that is: Xⁿ + 1 = X^(m+n)

In the simplest case n=1, let m=a:

X¹ + 1 = X^(1+a)

Then, changing a:

X+1=X² gives Φ and −1/Φ.
X+1=X³ gives the plastic number p=1.32471...
X+1=X⁴ gives 1.220744... and −0.7244919... (related to √(2/3)).

X+1=X⁰ gives X=0.
X+1=X⁻¹ gives X=−Φ and 1/Φ.
X+1=X⁻² gives X=1/p (plastic number).

So the plastic number also appears quickly.
It comes later than Φ, but is also a basic number

....Probably..it may be.

.....But, oh?

X+1=X¹

what then???

（to be continued)

Tanu-chan💓　TOKYO-TANUKI💛