The Giza Plateau
Exploring the amazing mystery of the Giza plateau, looking into the mathematics and geometry of the pyramids.
The location of the Sphinx is related to the golden ratio (phi), as seen below.
The Egyptians used the golden ratio (phi) everywhere.
“Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio (phi). The first we may compare to a measure of gold; the second we may name a precious jewel.” Johannes Kepler
The causeway of Khafre and also the causeway of Khufu are the same angle and are represented by the red triangle.
Using what we learnt from Khafre to visualize the geometry of the causeway angle.
The Mathematics of the Giza Plateau
The three Great Pyramids Khufu/Cheops, Khafre/Chephren and Menkaure/Mykerinos, each seem to contain lots of mathematics.
As we will see, Khufu and Menkaure are in essence the ‘same’ pyramid just at a different scale; meaning that they both have the same angles. Khafre (the middle pyramid) is the key to understanding the mathematics of the other two pyramids.
The Three Pyramids of Giza
The mathematics of the 3 main pyramids at Giza. (3 wise men?)
- The Khafre/Chephren or middle pyramid.
- The Menkaure/Mykerinos or small pyramid.
- The Khufu/Cheops or great pyramid.
When trying to find actual measurements, we find many varied numbers, so it is impossible to be 100% accurate. (numbers in feet)
- Menkaure (226, 178, 288).
- Khafre (472, 354, 590).
- Khufu (480, 378, 611).
Again, assuming the height of the Khafre relates to the number (2), we can divide the numbers by half the height of Khafre (472/2 = 236), to get the following ratios.
- Menkaure (226/236, 178/236, 288/236).
- Khafre (472/236, 354/236, 590/236).
- Khufu (480/236, 378/236, 611/236).
Interestingly the number 236 could be based on the square root of five (√5 − 2), just like the golden ratio (phi) which is found all over the Giza plateau.
If we compare the numbers, we notice a very interesting relationship between the three pyramids of Giza.
- 226/236 = 0.958 compared to A₁ = 0.971 (99% accurate)
- 178/236 = 0.754 compared to B₁ = 0.763 (99% accurate)
- 288/236 = 1.220 compared to C₁ = 1.236 (99% accurate)
- 472/236 = 2 compared to A₂ = 2 (100% accurate)
- 354/236 = 1.5 compared to B₂ = 1.5 (100% accurate)
- 590/236 = 2.5 compared to C₂ = 2.5 (100% accurate)
- 480/236 = 2.033 compared to A₃ = 2.058 (99% accurate)
- 378/236 = 1.601 compared to B₃ = 1.618 (99% accurate)
- 611/236 = 2.589 compared to C₃ = 2.618 (99% accurate)
Here we can more clearly see the mathematical relationship between the three pyramids and the ‘cosmic’ equation.
The Hidden Pyramid
The amazing relationship between the three main pyramids at Giza.
- The Menkaure pyramid (A₁, B₁, C₁).
- The Khafre pyramid (A₂, B₂, C₂).
- The Khufu pyramid (A₃, B₃, C₃).
- The ‘hidden’ pyramid (A₄, B₄, C₄).
In the numbers, we find a ‘hidden’ pyramid with the same height as Khafre and the same angles (essence) as both Menkaure and Khufu.
“Simplicity is the ultimate sophistication.” Leonardo da Vinci
Read more : The double (red and blue) triangle formation, circle and the square.
For the Egyptians, it seems the ‘cosmic’ equation was most important. Probably the source of what is now called Pythagoras formula.
Two circles (1/x) and (x) interact to become two sides of a right angled triangle, with hypotenuse (x+1/x) and base (x−1/x) and with height always equal to the number (2).
Each pyramid at Giza relates to a different version of this magical equation.
This is very interesting because it gives us a different way to
They knew that the reciprocal of zero (0) was infinity ().
The capstone of Khufu, represents the whole of the pyramid pointing at the fractal nature of the numbers.
As above (macro, large), so below (micro, small).
The Kings Chamber
The Kings chamber contains two triangles, the 3-4-5 triangle and the 2-3-√5 triangle.
The 3-4-5 triangle is the same as the ratios of the Khafre pyramid.
Sir Flinders Petrie reported that the floor of the Kings chamber was inset from the walls, and thus the walls can exhibit two heights; one to the floor surface (17 feet) and one to the true base of the wall (19.007 feet).
The inset in the Kings chamber seems to be based on the square root of five (√5 − 2).
Possibly pointing to metallic mean (number 4).
Five and its Square Root
As we have seen, the numbers 3, 4 and 5 represent the middle pyramid and point to the ‘cosmic’ identity.
The number 5 or more precisely the square root of five (√5) is found all over the Giza plateau, lets try and find out why. As we can see below, we find the root of five in both the 1st and the 4th of the metallic means or ‘cosmic’ numbers.
- (√5)/2 ± 1/2 = 1.618 (x) and 0.618 (1/x) where x−1/x = 1.
- √2 ± 1 = 2.414 (x) and 0.414 (1/x) where x−1/x = 2.
- (√13)/2 ± 3/2 = 3.303(x) and 0.303 (1/x) where x−1/x = 3.
- √5 ± 2 = 4.236 (x) and 0.236 (1/x) where x−1/x = 4.
The nature of the square (four equal sides). Interestingly we can cut a square into both four equal triangles or squares.
Also, we can cut a square into both five equal triangles or squares.
The fractal nature of the pentagon (five equal sides).
- The Mathematics of the Giza Pyramids and Plateau.
- The Symbolism of the Giza Pyramids and Plateau.
Read more : Unknown Squared Circle