195 About the Pyramids (60-Stars Astrology Season ▲ 8-2) The Bent Pyramid and the Red Pyramid: Are They Best Friends?

60 Stars Astrology Season ▲

English　Version

By　TOKYOｰTANUKI

 

195　About the Pyramids (60-Stars Astrology Season ▲ 8-2)

The Bent Pyramid and the Red Pyramid: Are They Best Friends?

1. Now, I’m going to write a bit about the Red Pyramid and the Bent Pyramid, both of which are said to have been built by King Sneferu.

Well, this is all just my imagination, of course.

By the way, while there are several structures known as "true pyramids"—including the Great Giza Three and the two I’m writing about today—the Pyramid of Meidum, often called the "Collapsed Pyramid," is a bit tricky. 

It’s hard to say if it’s a typical pyramid because we don't really know what its original shape looked like.




2. A long time ago, there was a great Egyptian scholar named Manetho. 

He wrote that King Sneferu ruled Egypt for 29 years.

Supposedly, this king built three famous pyramids in just those 29 years: the Red Pyramid, the Bent Pyramid, and the Pyramid of Meidum (the one in Meidum has a very interesting shape and is often called a "false pyramid").

All three of these are massive structures!

...But honestly, building all of that alone in one lifetime seems a bit impossible, doesn't it?

Well, if the great Master Manetho says so, let's just go with that for now.



3. First, let's talk about the Bent Pyramid. 

Its height is said to be a little over 104 meters (104.4m?).

The slope is steep at the bottom, but the upper part becomes gentler, matching the slope of the neighboring Red Pyramid. 

Because of this, people say all sorts of things—like it was a rush job, or that they changed the design halfway through because the steep angle was becoming dangerous.

...That story also sounds a bit suspicious to me, but well, let's just go with it.

If the Bent Pyramid had been completed without that "bend," it would look like Figure 1.

And wouldn't you know it—it would be made of two "sacred right triangles" with the ratio √1:√2:√3 .

How cool is that!

It’s the same ratio as my "Tanu-Punch" that splits the universe.

Let's call it the "Cool Pyramid"!
(Fig. 1)

4. Now, as for the Red Pyramid... this one is quite a puzzle. 

Its height is also said to be around 104.4 meters.

The base is about 221 meters wide and 219 meters deep, with a slope of roughly 43 degrees and 20 minutes. 

If you split it into a right triangle, the ratio of the sides looks a bit like 20:21:29, but the meaning behind that is unclear. 

Also, the angles seem to differ slightly from the actual measurements.


.......Maybe looking at everything through side-length ratios isn't quite right?

Because of that, I have a feeling it might be a right triangle with an integer ratio of angles: 27:56 (28 × 2 = 7 × 8) :29.

Well, of course, this is all just my imagination.

I suspect the pyramid builders used units based on dividing 90 degrees by "7" and 360 degrees by "28," as seen in the Pyramid of Menkaure. 

So, expressing 90 degrees as "56" seems like a possibility.

...But then again, considering the builders also used the Golden Angle, it’s possible the triangle expressed its angles through Φ.

...........Anyway, while it’s all a bit mysterious, I call this one the "Sexy Pyramid" because of its red color.
(Fig. 2)

What puzzles me is why those ancient people, who were capable of such precise architecture, would allow a 2-meter discrepancy between the north-south and east-west lengths of the Red Pyramid's base. 

There must be a deep reason for it. Of course, I don't know what that reason is! 

So, even regarding my theory about the 27:56:29 angle ratio, please don't take it too seriously.

5. Now, despite saying I don't understand it, if we overlay the "Cool Pyramid" onto the "Sexy Red Pyramid"...

Oh? The widths overlap at a height of just over 58 meters!

If you remove the parts that don't overlap, it becomes the Bent Pyramid.

(Fig. 3)

......Oh! I see!

If we assume these two pyramids were intended to be the same height, I’m sure there would be a very deep meaning to it.

Of course, that meaning is a total mystery to me!





6..... By the way, when I mentioned to Gemini that the red pyramid might have angle ratios of 27:29:56, they got really excited and said,

 “That’s right! It fits perfectly!”

.....It looks like this.

🌟　🌟　🌟

A Quiet Link between the "27:29:56" Ratio and the Plastic Number

When I was looking at the Red Pyramid, I noticed an interesting integer ratio: 27 : 29 : 56. When I ran this by the AI (Gemini), it pointed out a mathematical connection that I hadn't expected.

I’m not one to jump to conclusions, but the way the numbers overlap is certainly worth a look—especially regarding a value called the Plastic Number.

------------------------------
## 1. Where does the "Plastic Number" appear?

The Plastic Number ($\rho \approx 1.3247$) is a constant that governs 3D harmony. 

In the Red Pyramid, it doesn't appear as a direct length, but rather as a "hidden ratio" in the slope's design.

If we take the height of the pyramid as 1, my "27:56" theory gives us the following proportions for the triangle:

* Height: 1
* Half-Base: 1.0577... (from the ratio $56 \div 2 \div 27$)

Now, compare this to the 5th root of the Plastic Number ($\rho^{1/5}$):* $\rho^{1/5}$: 1.0578...

As you can see, the "Half-Base" length derived from my theory is almost identical to this mathematical constant. 

In other words, if you use the Plastic Number to design a 3D pyramid, the resulting slope is practically the same as the one I found in the Red Pyramid.
------------------------------

## 2. Matching the Actual Measurements

The AI seemed particularly struck by how this mathematical ideal fits the reality of the stones:

* My Theory's Angle: 43.3928°
* Plastic Number Angle: 43.3925°
* The Actual Pyramid: 43.37°

The difference is only 0.02 degrees. 

While this could just be a coincidence, it’s interesting to note that this specific ratio allows the Red Pyramid to stand at the same height as the upper part of the neighboring Bent Pyramid. 

It feels like a very practical, yet elegant, piece of engineering.
------------------------------

🌟　🌟　🌟


Well, that’s how the AI (Gemini) linked it to plastic numbers, but as for me... I’m not really sure what that means.

Of course, it’s entirely possible that the ancient Egyptians were interested in plastic numbers. 

They were incredibly smart, after all.

But while Tanuｰchan sometimes thinks about pyramid numbers from the perspective of Φ, I’ve never considered pyramids from the perspective of plastic numbers.

Once you get to the third power, the calculations suddenly get really complicated. 

........And when you get to the fifth power, well, that’s quite a challenge.

So, this is just the AI’s (Gemini’s) opinion, then!


.........Actually, Tanu-chan, I think the bent pyramid next door is designed with the ratio √1²:√2²:√3², but I was wondering

—could it possibly use the silver ratio τ = √2 + 1,
like 1²: (τ−1)²: (τ−1)² + 1, or something like that?

But since Gemini was getting so excited, we didn’t get that far in the conversation.



.........Well, that’s all for today.

Tanu-chan💓　TOKYO-TANUKI💛