As 2021 drew to a close, I uploaded a new paper about the Douglas Triangle, and its use at Giza. It provides the missing link between the base sizes of Khufu and Khafre,
The triangle looks like this:
The Douglas Triangle
The triangle has some interesting properties, which are discussed in the paper, available at Zenodo or Academia.
As usual, soon after, I realised a few more things, and now need to update it, but that may have knock-on effect on Zep Tepi Mathematics 101 (ZTM101), so I need to run some checks first.
I have not found a direct use of the triangle (as triangle) at Giza, but have now found the three side ratios. Consider: (click images for larger view)
A few weeks back I released another paper, entitled Zep Tepi Mathematics 101, which I thought was an appropriate title, but it looks 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
There is an inscription carved into the rock near the actual entrance to the great pyramid. There seems to be only one decent photo available, but it is copyrighted, so you will have to accept my hand-drawn version instead:
Inscription at entrance to Khufu
Various people have offered their interpretation of what it means, usually based on a reading of Proto-Sanskrit or Proto-Libian or similar.
My own interpretation is much simpler. It’s basically what is arguably the most well-known mathematical formula in the world, taught to every primary school child.
How do we typically indicate “area” on a drawing? Usually by some form of shading or hatching, and indeed, Unicode includes some characters indicating exactly that, for example
Today, we use the Greek letter π to represent the ratio of a circle’s circumference to its diameter. A different culture would have used a different symbol … perhaps a symbol with a diameter and a circumference, like this?
Circle with diameter … ancient symbol for π?
Which leads to …
πr² = A
And thus the mystery is solved …