℁ 60stars astrology Season ▲ Special Supplementary Lesson A Review of 4Φ⁶ and the Pyramid (Part 2)

60 Stars Astrology Season ▲

English　Version

By　TOKYOｰTANUKI

℁ 　60stars astrology Season ▲ 

Special Supplementary Lesson

A Review of 4Φ⁶ and the Pyramid (Part 2)

1．As we have already seen, the pyramid seems to make frequent use of numbers such as Φ, ∛3, and √2.

When you start using these numbers in calculations involving cubes and rectangular solids, your eyes gradually begin to hurt!

Well... I honestly don't know why the ancient Egyptians chose to do things this way.

Even Panda-chan is shaking her head.

(Fig. 1)

And then...

I also think that people who studied the pyramids—including Leonardo da Vinci—understood how to convert these expressions for the circumference into the familiar system where 360 degrees represents one complete circle.

Da Vinci, in particular, left us drawings, which makes the idea much easier to understand.

The quantity【（√５－２）/２】which appears in his construction, is what Tanu-chan calls the Da Vinci Number.

.......Here is a quotation from an earlier article.

..........................

In the previous post, we found that

（√5-2)/2 = 0.118033988.... 

Interestingly, the expression √5 − 2, which appears in Leonardo da Vinci's drawing, also appears in the geometry of the Φ-gon.

The same quantity can also be found in the King's Chamber of the Great Pyramid.

In that sense, the King's Chamber and the Vitruvian construction may share the same geometric composition.

If that is true, then Leonardo da Vinci may have understood the relationships among circles, polygons, polyhedra, and spheres remarkably well.

 

...............Of course, I am only a humanities student, not a mathematician, so I look forward to the day when some genius kindly explains all of this to me.

Anyway...

Let us call the value（√5-2)/2 = 0.118033988.... ,

the Da Vinci Number.

(Fig. 2)

2. And then...

I also think that the people who designed or studied the pyramids understood how to convert between Φ and ∛3, two numbers that appear repeatedly throughout the structure.

I wrote about this before, so let me quote that article again.

...................

√5-2)/2 = 0.118033988.... 

The numbers shown in Mr. Da Vinci's picture “√5-2” are also found in φ-gon.

This number is also found in the King's Chamber of the Pyramid of King Khufu. 

We can say that the King's Chamber and the Vitruvian figure are the same composition.

Then again, Mr. da Vinci may have fully understood the relationship between circles and polygons, polyhedra and spheres.

Of course, I am a liberal arts student, so I don't know much about figures, so I'll wait for the day when a genius shows up and kindly teaches me!

The number I just wrote 0.118033988... Let's call the number 0.118033988... the Da Vinci number! "
（図２）

３．　Furthermore, it is believed that those people understood the formulas for converting between Φ and ∛3, which are frequently used in the pyramids.

That’s why I wrote about it in this article. I’ll quote it again here.

..............................

 

"Multiplying the ratio of the outer size of the stone coffin to the inner size,

∛3 × ∜√3 × ∛√3 = √3^(2/3+1/4+1/3) = √3^(15/12) = √3^(5/4)
= 1.987013346421...

When this is multiplied by (2 × 2 × 2) = 2³ ,
1.987013346421.....^8 = 243 = 3^5.



This 243 is
243 ÷ 3⁷ = 0.1111111... = (1 ÷ 90) × 10
...which connects to the Da Vinci number.  

Additionally, when multiplied by 2^2^2,    
1.987013346421.....^16 = 59049 = 3^10 = 3^(5×2) = 243^2    is the result.    

People may have forgotten about the Da Vinci number, so I will repost the drawing I made in the past post.

Looking back at my past posts, I realized; Although I had written about the Da Vinci number, I had not clearly stated that it is a unit of measurement for circles, so I will make the drawing again.



Anyway...a circle is represented by 360 degrees（360°）.

Following the general method of expressing the circumference of a circle as Φ²,  the circumference can also be expressed as Φ⁶, which is its power.

  
When the circumference is set to 360° = 4Φ⁶ = 71.777...,  
1 degree is expressed as  4Φ⁶ ÷ 360 = 0.011111111........

Considering this value in relation to the ratio shown in Da Vinci's painting,   (√5—2)/2, or (√5—Φ—1/2), as the standard (Da Vinci number = d),   

it is expressed as 1 degree 

= 0.1111111... = (d⁻²)/(4Φ⁶ × (1/360)).  


By the way, as mentioned previously, multiplying the ratio of the inner and outer edge lengths of the sarcophagus yields √3^(5/4), and raising this to the 8th power results in 234.
And 0.01111... = 243 ÷ 3⁷ ÷ 10

Therefore, since 360 degrees of the circumference can be expressed as 0.011111... × 32,400, it is easy to perform the conversion using √3^(5/4).

....In other words, the circumference of 360 degrees can be expressed fairly simply using either the ratio of Φ(d = (√5 - 2)/2), or the ratio of the cube root of 3 (√3^(5/4)).  

Although it is a bit tedious, both the inner and outer edges of the pyramid's sarcophagus can be converted using units that indicate the circumference. "

(Fig. 3)

Using this ratio, it is also possible to construct a sacred equilateral triangle whose base angle is 1/Φ.

There is even a building in New York that seems to use this proportion.

Well...Chat-GPT insists that it is merely a coincidence.

(Fig. 4)

...To be continued again!

Tanu-chan 💓  TOKYO-TANUKKO💛