Papers

The Beautiful Cubit System

An analysis of the Egyptian Royal cubit, presenting some  research and opinions flowing from that research, into what I believe was the original cubit, and how it was corrupted. I show various close arithmetic approximations and multiple ways of getting the divisions of the cubit, as well as some related measures. The cubit also encapsulates the basic components for the metric system.

https://doi.org/10.5281/zenodo.3263863
https://www.academia.edu/40366556/The_Beautiful_Cubit_System


Diskerfery and the Alignment of the Four Main Giza Pyramids

The curious alignment of the three main pyramids at Giza has puzzled many people over the ages. Various theories have been proposed, either based on site geometry or stellar alignments coupled with known ancient Egyptian religious beliefs. This paper shows that the precise alignment of the pyramids can be explained with mathematics alone, using diskerfery and other geometry. We then use the same techniques to identify the most- probable location of the now-dismantled fourth pyramid at Giza. The techniques and discoveries in this paper provide the basis for dating Giza, as discussed in the companion paper “55,500 BCE and the 23 Stars of Giza” .

https://doi.org/10.5281/zenodo.3263926
https://www.academia.edu/39724917/Diskerfery_and_the_Alignment_of_the_Four_Main_Giza_Pyramids


55,500 BCE and the 23 Stars of Giza

This is a companion paper to and reliant on “Diskerfery and the Alignment of the Four Main Giza Pyramids” (Douglas, 2019 [1]). Following the geometric alignments shown in that paper, we now present the astronomical design plan with 23 stars. There is a perfect alignment with two stars, very close alignment with others, and close alignment with other prominent stars in the area. We propose that this was done to provide a date for the construction of Giza. The alignment occurs at circa 55,500BCE.

https://doi.org/10.5281/zenodo.3263927
https://www.academia.edu/41171982/55_500_BCE_and_the_23_Stars_of_Giza


The foot, cubit, metre, and φ, π and e

A short document highlighting the consistent relationship between the foot, cubit and metre, and combinations of them, and phi, pi and e, via e-1.

https://doi.org/10.5281/zenodo.4276327
https://www.academia.edu/44513464/The_foot_cubit_metre_and_%CF%86_%CF%80_and_e


Zep Tepi Mathematics 101 – How Giza was probably designed

A mathematics course from the Zep Tepi era, where we plan and analyse a large building site, showing how the design mirrors the stars.

A simple and elegant explanation of how Giza, with six main pyramids, was laid out, using √2, √3, √5, π and φ. The design incorporates the necessary elements for squaring the circle, area-wise. The design matches the heavens around 55.5k BCE. This could force a rethink of at least the history of mathematics, if not the broader human timeline, and effectively solves the puzzle of how Giza was laid out.

https://doi.org/10.5281/zenodo.4410650
https://www.academia.edu/68408866/Zep_Tepi_Mathematics_101_How_Giza_was_probably_designed_Version_1_2_0


Khufu’s Coffer

An analysis of Khufu’s coffer dimensions and location, based on Petrie’s measurements. The analysis suggests that it can not be 4th Dynasty, due to the formulas involved.

https://doi.org/10.5281/zenodo.5516434
https://www.academia.edu/52872809/Khufus_Coffer


Pi, phi and e in Khafre’s dimensions

Some formulas showing how approximations for pi, phi and e are in the dimensions of Khafre.

https://doi.org/10.5281/zenodo.5554990
https://www.academia.edu/56357876/Pi_phi_and_e_in_Khafres_dimensions


The Douglas Triangle, Khufu and Khafre

The Douglas triangle is a special right triangle using φ and √3. It appears that its proportions and peculiarities impressed the Giza planners so much that they used it, when scaled by 50π, for the base lengths of the Khufu and Khafre pyramids. This paper presents the triangle and discusses some of its interesting features.

https://doi.org/10.5281/zenodo.5810430
https://www.academia.edu/66612918/The_Douglas_Triangle_Khufu_and_Khafre


The Beautiful System

A one-page summary version of my “The foot, cubit, metre, and φ, π and e” paper, suitable for wall mounting or as a handy reference.

https://doi.org/10.5281/zenodo.6038713


The six pyramids and planets at Giza

In a previous paper, Zep Tepi Mathematics 101, and the ones it references, I showed how Giza had six main pyramids, with a mathematically designed layout, based on a stellar arrangement around 55.5k BCE. One “problem” with that proposal is that the sizes of the pyramids do not match the brightness of the stars. In this paper I show that the pyramid sizes actually correlate to the sizes of the six planets closest to the sun, with the pyramids arranged from west to east in increasing size order. This implies that the builders could accurately measure the diameters of the five planets plus Earth, as well as being aware of the four Galilean moons, and Saturn’s moon, Titan. This implies they had optical instruments like telescopes.

https://doi.org/10.5281/zenodo.6374281