櫐(ru-i) — 60-Stars Astrology Season ▲ Before Beginning the Individual Pyramid Articles

60 Stars Astrology Season ▲

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By　TOKYOｰTANUKI

櫐(ru-i) — 60-Stars Astrology Season ▲

Before Beginning the Individual Pyramid Articles

 1. Well, in this Season ▲, rather than trying to explain the pyramids, I'm simply going to write down my amateur thoughts and animal-like daydreams about them.

I'm planning to write mainly about what are generally called the "true pyramids".

First of all, I won't be writing about the Step Pyramid.

.....The reason isn't anything profound.
It's simply because I don't really know what its original shape was.

The Pyramid of Meidum is easier, because its failed reconstruction lets us guess what it originally looked like.

The Step Pyramid, however, seems to have been rebuilt several times.

So I honestly don't know what its original form was.

And if I don't know that, I don't really know what to write.

2. As for the three great pyramids at Giza, I describe them like this:

Khufu: side-length ratio = 1 – √Φ – Φ
Khafre: side-length ratio = 3 – 4 – 5
Menkaure: angle ratio = 3 – 4 – 7

At this point, some readers may wonder,

"Why is only the last one described by angles?"

Well...

I could certainly describe it using lengths if I wanted to.

For a regular heptagon with side length 1,
the shorter diagonal is 

a = 1.8019377...
and the longer diagonal is
b = 2.246979...

These satisfy
ab = a + b

Later in this season, I'll also explain that
a² = b + 1

Since b = a² − 1,
the value of "a" is a root of the cubic equation
 a³ − a² − 2a + 1 = 0.

Now, a right triangle with the angle ratio 3–4–7 appears inside a regular 14-gon.

Every diagonal of the regular 14-gon can be expressed using this same value "a=1.8019377...".

Likewise, the triangle with the angle ratio 3–4–7 has side lengths
(a + 1) : (a² + a − 1) : (a² + a − 2) : (2a² − 2)

...........So it can also be written rather neatly.

The same thing happens with the regular 28-gon.

Every diagonal can be expressed using the same number "a", and it becomes possible to construct some rather elegant right triangles that geometry enthusiasts tend to enjoy.



3. Based on the measurements I've examined,
I'm fairly convinced that the angle ratio of Menkaure's pyramid really is 3–4–7.

And perhaps...
perhaps it points toward the Lucas sequence....

But I'm still holding back a little.

The reason is simple.

I'm fairly sure that the sequence
1 – √Φ – Φ
has something to do with curves and the way we count them.

And I'm also fairly sure that
3 – 4 – 5
has something to do with straight lines and polygons.

But 3 – 4 – 7...
What exactly does it count?
What is the object being counted?
I honestly don't know.

......Many people know that sunflower seeds often follow the Fibonacci sequence.

In fact, about five percent of sunflowers seem to follow the Lucas sequence instead.



Hmm...
I still don't really understand.

What kind of things is this sequence actually used to count ???

Since I don't know,
for now I'll simply describe it as the angle ratio 3–4–7.

If I discover something later,
I'll let you know.

.....Although...to be honest, I'm not very optimistic.



Anyway, that's the assumption I'll be working under throughout this season.



That's all for today.

Tanu-chan 💓 TOKYO-TANUKI 💛