Elegance defined

Even though I’ve been staring at these numbers and relationships since 2018, I only tumbled onto this sequence this week. Those Egyptians loved mixing their units of length into irrationals.

The sequence is this, it’s a set of ratios:

F : ₢ :: 1 : é :: ℳ : φ² :: ₷ : π.

where
F = foot 0.3047 m (probable original length, not 0.3048 as declared now)
₢ = royal cubit 0.5236 m
1 = 1 metre
é = e – 1 = 1.71828…
ℳ = 1 + ₢ = 1.5236 ( == 5 feet)
φ² = golden ratio squared
₷ = six feet = metre + cubit + foot
π = pi.

Approximating the Fine Structure Constant (again) aka There’s Something About φ

While poking around Giza, I stumbled on this approximation for the inverse of the fine structure constant. It’s not as good as my previous one, but since it relies on cubit -> metre conversion, it qualifies as “interesting.”

It’s just 100φ² ₢, expressed as metres, So we just multiply that by π/6, and voila!

137.0799391

Which according to Wolfram Alpha,

100 / (100φ²π/6) / (fine structure constant)

is 99.9679457% accurate …

Well, according to the current known value, which is a moving target.

Approximating the Fine Structure Constant

The fine structure constant is described as one of the most fundamental physical constants. I don’t pretend to understand anything about it apart from its value, which is close to 1/137. We’ve only been using it for around 100 years.

So the fact that the Khafre pyramid uses 137 as a size multiplier (base is 3 x 137, height is 2 x 137) is annoying, especially since the Khufu pyramid references the speed of light in metres per second, twice. The ancient Egyptians are not supposed to know those things.

Since the fine structure constant itself is a messy decimal number (0.0072973525693…) it is usually referenced via its inverse, as 1/137, which provides a reasonable approximation.

However there have been attempts to find a better approximation, and Scott Onstott has a page with some approximations. Which naturally was a challenge I could not resist….

So I saw that one of the better ones was based on 137²+π²…. and since the royal cubit is π/6, and I have lots of approximations for that, it was simply a matter of finding the right one that produced a better result. That turned out to be based on the plastic number… so without further fanfare, here we are:

\frac{1}{\alpha} \approx \sqrt{{137^{2} + (\frac{\rho^{9}}{4}})^{2}}

 

The WolframAlpha version of the formula is √(137² + ((plastic number^9)/4)²), which produces

137.0359992970725102075551820936909082242952278384186387671

We can check the percentage accuracy as well:

100/137.0359992970725102075551820936909082242952278384186387671 / (fine structure constant)

produces 99.9999998% accurate. Not bad.

 

 

The Secret is as Simple as e

I updated my paper on the alignment of the pyramids again, and included some new diagrams. The most important of which is this stunning bit of simplicity. As a reminder. ⦦e means “360/e”, which is 132.437°. The pure elegance of this may be disruptive to existing theories about the alignment of the pyramids. You read it here first 🙂  (Always wanted to say that.)

How the pyramids are aligned, based on e

You can see the paper itself for the accuracy table. Two are accurate to less than 0.1° and the other is below 0.3°.

408, 199 and 159

A follow-up to the 437 post, this time applying the same methodology to Khafre and the other two pyramids.

If you have seen my papers then you will know that Khafre is often connected to the number 3. This same idea pops up here.

So …. Khafre has a base length of 411 ₢. 411 – 3 is 408.

If we had a square with side 408, then the diagonal would be 408√2, or 576.999.

If we divide 1000 by that (a process which effectively takes the inverse, and fixes the location of the decimal point), then we get

1000/576.999 = 1.733104858, which is a close approximation of √3 … it differs by 0.0010540… Accuracy is of course limited by having to start with whole-cubit dimensions.

I have tried the same approach with the other two pyramids, as follows. SInce we are using smaller dimensions to start with, accuracy does suffer a bit:

Continue reading

437

While playing around with the calculator, looking at relationships between the numbers at Giza, I took another look at the diagonal of the great pyramid.

The great pyramid has a base of 440 ₢. This means the diagonal is 440√2, which is 622.25 ₢. This is about 4 ₢ more than 1000/φ, which is 618 ₢. The error percentage is about 0.6%, which is annoyingly close.

So I got to wondering what base size would produce a diagonal more or less exactly 1000/φ.

The answer turns out to be 437, which is 3 ₢ less the existing size.

437√2 = 618.011 which is as close as you are going to get using whole-cubit dimensions.

But the oddness does not stop there.

Continue reading

Publish or perish!

Well, I’m not in academia, so I won’t perish, but I have spent the last few months discovering some things about Giza which I didn’t post here. Instead I posted them as papers online (because I really don’t like the Academic Publishing business model, and probably would not have been accepted by any ‘proper’ journal anyway, because what I say is rather history-shattering…)

So the first paper was a round-up of stuff posted here, relating to the cubit:
The Beautiful Cubit System

While the other two are companion papers that rely on each other to a degree:
Diskerfery and the Four Main Giza Pyramids and
55,550 BCE and the 23 Stars of Giza

The important images are below, read the papers to get the full story 🙂

Continue reading

Phi redux

I started poking around Giza and ancient Egypt after watching a video on the Nebra disk, and trying to find a similar circle-split-by-phi in the alignments of the Giza pyramids.

I didn’t find what I was looking for at the time (in terms of phi being in the alignment of all three pyramids) but did find lots of other things, including phi between P1 and P3.

In the mean time, the so-called Genetic Disc from Peru came along, and I immediately noticed a similar division there. Here’s the two sides of the disk:

Genetic disk from Peru

Continue reading

Playing with numbers

Playing around with the great pyramid.

Length of base + height = 440 + 280 = 720 royal cubits.

720/360 = 2 (save this for later)

If we convert to digits by multiplying by 28 (because 28 digits in royal cubit), we get

720 x 28 = 20160

If we divide by 360, we get

20160/360 = 56, which is the number of digits in 2 cubits (see saved value of 2)

As you may know, I’m developing a theory that whoever came up with the cubit system also divided the circle into 336 Zeps. So if we divide by 336 instead….

20160 / 336 = 60

Which is um, all sorts of things, and maybe a hat-tip (or the finger) to the Sumerians and their sexagesimal system.

But what the 60 also equates to, is if you had a wheel of radius 1 metre, then 60 rolls of the wheel would equal the sum of the side and the height.

If your wheel had a diameter of 1 metre (like a chariot), then it would be 120 turns of the wheel. Exactly.