Mathematical Encoding in the Great Pyramid
The Great Pyramid of Giza, the oldest and sole surviving Wonder of the Ancient World, has attracted the interest of philosophers, savants, and travelers for at least four millennia. Some of this interest has centered on the question of whether the ancient Egyptian culture possessed and encoded certain mathematical concepts in the pyramid’s proportions and measurements.
I have analyzed the Great Pyramid’s geometry without considering the issues of what mathematical knowledge ancient Egyptian architect-engineers did or did not authoritatively possess. If ancient designers did encode something in the Great Pyramid, I believe they would have wanted the structure’s very geometry to carry the message.
Perhaps the Great Pyramid is not a tomb but a tome—open to all those who possess geometrical understanding, much in the same spirit of what Plato’s Academy inscribed millennia later on its door, “Let no one ignorant of geometry enter.”
The Great Pyramid’s elevation encodes three of the most important constants in mathematics: π, Φ, and e. The slope angle of 51°51’ (51.85° in decimal form) comes from measurements taken off the remaining casing stones, according to detailed survey data from Flinders Petrie and J.H. Cole .
You can verify these encodings with the following equations. The accuracy percentage for each equation is given in parenthesis.
4 x 51.85° / 76.30° = e (99.998%)
tan 51.85° = 4 / π (99.99%)
cos 51.85° = 1 / Φ (99.95%)
sin 51.85° = 4 / πΦ (99.94%)
The constant e, known as Euler’s number, wasn’t discovered until 1618. Consider the possibility that this was merely rediscovery. We are generally so accepting of the myth of linear progress that it is easy to forget that sometimes knowledge is lost and not rediscovered for a very long time, if ever. For example, it has been said that the plumbing system in the palace of Knossos, Crete built in 1900 BCE wasn’t matched until circa 1900 CE in England.
Another way of looking at the Great Pyramid is by analyzing its relative proportions. If the base measures unit length then a square with an equal unit edge can be drawn as shown below. A circle drawn from the center with radius equal to the height of the pyramid has a circumference equal to the square’s perimeter. Thus, the Great Pyramid “squares the circle.” Its form approximates the solution sought by ancient geometers, who for many generations endeavored to square the circle by length (squaring a circle by area is a related problem). Note: exact squaring of the circle is impossible due to the transcendental qualities of π (proved by Lindemann in 1882).
In addition to relative proportions, I wondered if the Great Pyramid might encode anything in absolute units? To find out, I drew its elevation in a computer aided design program in actual size, according to J.H. Cole’s surveyed values (I used 755.775 feet for the mean base edge length).
I rediscovered many layers of encoding in the Great Pyramid by taking its precise measure and looking for patterns. If you inscribe an equilateral triangle inside, this is what immediately pops out: the green triangle’s edge length is 555.5 feet, or 6666 inches. This distance happens to match the height of the Washington Monument and the length of St. Paul’s Cathedral but that is another story (to learn more see my video series, Secrets In Plain Sight). The key pattern to observe is the repeating digits, even though it goes against what we think we know about the English foot’s provenance.
Another method of analyzing the pyramid geometry is with a square rotated 45° with respect to the ground plane. The largest such square that fits inside the pyramid’s elevation encodes two circles across its diagonal, having circumferences equaling exactly 666.6 feet each, allowing that the slope angle of 51°51’ has an accuracy of only 99.8%.
If you circumscribe the pyramid’s elevation triangle and then measure the circle’s diameter, this equals 777.7 feet (99.97% accurate with a slope of 51°51’ and base length of 755.775 feet). In addition, the inscribed circles shown below in red and blue have circumferences of 777 feet and 7777 inches, respectively. Sevens abound!
This next image depicts a single inscribed circle having a diameter of 365.242 feet inside the pyramid’s elevation that echoes Earth’s tropical year of 365.242 days. The circle’s exact diameter is 2.2 feet longer than this measurement, but this small delta might reference the Earth’s atmosphere, which is like an onionskin at this scale, roughly equaling the thickness of the diagram’s lines.