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:
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°.
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.
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 I’m watching a video from 2012, featuring a young-looking Graham Hancock
Which, before they got all wooshie about the Mayan 21 December 2012 end of the world thing, had some interesting info. In particular, the observation concerning the difference between two sides of the great pyramid, and its height, which goes like this:
two side of pyramid = 440 x 2 cubits. In metres, that’s 460.7669 m.
height of pyramid = 280 cubits = 146.6077 m
Difference = 460.7669 – 146.6077 = 314.1592 which you may recognise as 100 times pi.
Some updates to the zeptractor, probably done for now until I figure out if this was just a humongous waste of time or not. Well at least I got to learn something about svg drawing.
1. added assorted famous regular polygons: triangle, square, pentagon, hexagon, heptagon, octagon, dodecagon.
2. resized inner circle to divide radius in golden ratio. Also marked where circumference would be divided in golden ration (both directions, measuring from zero).
3. added radian marks (up to 6, only in normal direction).
4. added tau divisors … they’re more logical than the pi divisors. Arial has a sucky tau symbol.
5. put phi symbol on bare radius to avoid confusion.
The zeptractor, the tool for people who really know their way around a circle.