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:
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
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.