A few weeks back I released another paper, entitled Zep Tepi Mathematics 101, which I thought was appropriate, but it llooks like it was a bad choice and is not appealing to the target market.
The first part is actually a simple explanation of how the Giza site was laid out, using mostly √2, √3, and √5. No Orion required.
You can find the latest version at Zenodo (current version is 1.1.0), and also at Academia.
Here are some of the more important images discussed:
Six pyramids aligned, 55.5k BCE
I haven’t post anything in a while… got caught up with keyboard layout optimisation again, but am now back detangling Giza.
My guides nudged me to stumble across this last night.
At first I was flabbergasted, I was stunned…
Kept thinking I could not be the first …
Meawhile I got the distinct impression my guides were doubled over with laughter …
Rechecked the calculation on Wolfram Alpha (full values, rounded values) but it’s right… Using the rounded values, the answer is 1618.0049443… or 1618 rounded.
Asked Google who else has seen this but could not find anything … if you know, please leave a comment …
So this is a somewhat cryptic image … those “skilled in the art” will immediately understand what it is about and what it means.
The dimensions of the rectangle are thanks to John Legon.
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.
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.
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°.
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:
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.
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 🙂
Updated versions of the different ways of approximating the cubit. Also includes separate table for Grand Metre (1 plus royal cubit) == 1.5236…. == 1.524.
These are done with pi, phi, e, roots and powers (usually of basic primes), as well as ln, log, sin, cos and tan.
See square roots, cube roots and ln(4) for formulas not shown below.
Changelog at the bottom.See also The Magical Mystical Royal Cubit for the Pretty Picture version.
To borrow a phrase from Robert Bauval, this falls under the Spooky Stuff category.
It is a very strange connection between the Grand Metre (1 + royal cubit), the base of the natural logarithm ⅇ, and the royal cubit as measured in inches.
2018-11-29: added Spooky Stuff 7 and 8
2018-12-03: added Spooky Stuff 9
2018-12-04: added Spooky Stuff 10
2019-04-24: added Spooky Stuff 11
Royal cubit, e and inch
I have no explanation for this. It just highlights again the ancient origins of the metre, inch and royal cubit, and how they mysteriously link together with π and ⅇ. But what about φ you ask?…. here you go:
There are still some things that bother me about the Royal Cubit, in particular, why did they choose π/6, and why did they use it in preference to the metre.
Something interesting related to the first question has surfaced. Which may just be another random co-incidence like all the others, or maybe not.
First up, a reminder that the Royal Cubit is ⅙ of the circumference of a circle with diameter 1 metre, in other words the arc on a 360/6 = 60° segment, as follows:
As you may know, the ancient Egyptians were very fond of their ankh, which looks like this: