Φ³³ 60stars Astrology Season Essay Numbers and Delusions: A Strange Test "The Answer to the previous Questions ３"

60stars  Astrology Season  Essay

English  version

By TOKYO-TANUKI

Φ³³　60stars Astrology Season Essay 

Numbers and Delusions: A Strange Test 

" The Answer to the previous Questions ３ "

1.  This time, the Questions 3 were truly difficult—even if you could write the formula in Φ, it might be not easy to determine what kind of shape it represented.

The answer is this: on the boundary with chaos, there exists a form expressed as 2Φ⁷ + 2Φ⁴ ( = 4Φ⁶ ).

It is, so to speak, a solid that crumbles like sand. 

It still has a form, but it is already disintegrating. 

It can be said to be round, yet also angular, because its edges appear as it collapses.

2.  By now, many of you have probably noticed:

For the third type of solids—those derived from the cube—if we start from the sphere, we obtain:
4Φ⁶ ⇒ 6Φ⁵ + 2Φ² ⇒ 10Φ⁴ + 2Φ ⇒ 16Φ³ + 4 ⇒ 26Φ² + 6(1/Φ).

If we denote the coefficient of Φ as "A", then each new value of "A" is the sum of the previous two.

Thus, if the previous terms were "A" = 26 and "A" = 16, the next is "A" = 26 + 16 = 42. 

Hence, the next form of  "26Φ²+6(1/Φ)"  becomes "42Φ + 10(1/Φ²)" .

.....Meanwhile, for the second type of solids—those derived from multiples of 12—starting again from the sphere, we have:
4Φ⁶ ⇒ 4Φ⁵ + 4Φ⁴ ⇒ 8Φ⁴ + 4Φ³ ⇒ 12Φ³ + 8Φ² ⇒ 20Φ² + 12Φ.

If we express these as P₁Φⁿ + Q₁Φⁿ⁻¹, then the next coefficient P₂ is the sum of the previous Ｐ₁＋Ｑ₁ values. 

Therefore, since 20 + 12 = 32, the next term of  "20Φ²+12Φ" is "32Φ + 20"  (the soccer-ball-shaped solid) .

3.  In this way, we can see that 2Φ⁷ + 2Φ⁴ belongs simultaneously to both the the Group of Three and the Group of Two. 

So it is both rounded and edged—a form that is, in fact, disintegrating.



The next in the sequence would be: 2Φ⁸ − 2Φ⁵ ( = 4Φ⁶ ), and after that, Φ⁹ − Φ³ ( = 4Φ⁶ ).

These, however, no longer possess any tangible form in this world. 

...And Φ⁹ is the final term.

If one insists on describing it, it might resemble something fine and granular, floating upon a sea-like expanse. 

"It seems to drift upon the ocean or so" , ..... I was told by a friend.





4.  Why does the sequence end at Φ⁹? 

In truth, Φ⁹ − Φ³ represents the last faint trace of “form” visible within chaos—beyond that, nothing can be perceived by us.

……Now, this delusional test comes to an end. 

There is, of course, no need to get the answers right.

Incidentally, while I was compiling this table, one thing kept bothering me: the rhombus. 

I’ve long insisted that rhombi should be included among regular polygons, though it’s not a popular opinion.

Still, I can’t help feeling that there must be a way to express rhombic polyhedron within this system too. 

If I ever figure it out, I’ll be sure to write about it.

.....That’s all for today.  The test of delusion has ended.

Next time, in the last third of March, I will begin, 

" Season Vacation " !

............Maybe!


Tanu-chan 💓  TOKYO-TANUKKO 💛