(Based on an excerpt of Karl-H. Homann's manuscript "Und Sie Dreht Sich Doch Um Sothis", © 1996)

For the Original German Version, please click here.

It is assumed that the builders of the Great Pyramid had insufficient knowledge of the number Pi (p ). Paradoxically though, Pi is used to justify the statement of the Greek historian Herodotus, who recorded that the surface area of each face of the pyramid is equal to the square of its height. Apparently, Egyptian priests revealed this crucial piece of information to Herodotus.

Had the pyramid been built according to the Pi relationship, the above statement would indeed be 99.9% true. But it can also be assumed that the designers of the pyramid were not content with "approximately" 99.9% and that the mathematical term "equal" meant for them 100%. If this holds true, it would shed a completely new light on the knowledge and wisdom of its designers.

From R. A. Schwaller de Lubicz, the brilliant Egyptologist, we learn that in ancient Egypt temples and other buildings were designed and constructed according to the proportions of the golden mean. Would this also apply to the Great Pyramid?

Just by visually comparing the Great Pyramid with the other two pyramids on the Giza plateau, its precision is immediately apparent. Whether inside or outside, all its dimensions, orientations and angles are perfect. Granite blocks, weighing up to 70 tonnes, were cut precise to one tenths of a millimeter. But one of the main characteristics that differentiates it from all other pyramids is the so-called King's chamber situated at exactly one third of the pyramid's height. The so-called sarcophagus, crafted from a single piece of granite, is aligned towards north. And like certain segments of the four "airshafts" that are also carved in granite, it is of extreme precision. Despite our modern technology it would be extremely difficult, if not impossible, to reproduce it in such a quality.

In 820 AD Kalif Al Mamun was the first to succeed in an attempt to enter the Great Pyramid by force. Since no jewels or gold were found in the pyramid, one can be certain that no king or pharaoh was ever buried in there. What purpose could this mysterious chamber have served?

The Great Pyramid has always been a great enigma for mankind. While certain speculations may have led some folks to the right conclusions, scientists demanded proof. Yet with their so-called "well-established" theories and models they were standing still and asserted that none of the measurement and number theories hold up under scrutiny. Because a direct relationship with the number Pi was sought, it only led to insufficient mathematical approximations and wrong assumptions.

The highly disputed angle of inclination or slope of the Great Pyramid ranging anywhere from 51° 51' to 52°, as well as the no longer measurable height (estimated to be 146 to 147 m), contributed to further speculations. Unfortunately, for whatever reason, science never acknowledged the fact that the ancient Egyptians were well aware of the hermetic rule of the golden mean. Because if we were to apply the golden mean, also known as the Phi (j) relation, to the Great Pyramid, Herodotus' statement will appear under a completely different light. As a matter of fact, the assertion that the surface area of each face of the pyramid is equal to the square of its height can be mathematically verified (see appendix below).

What is Phi?

Phi is an irrational number that is usually derived from the so-called Fibonacci* series. However, it can be more accurately determined as shown in Drawing 23. The length of the square's side is a =1, resulting in r₁ = Ö 1,25 = 1.11803398.... . By adding half the length of a, we get the value of Phi of 1.61803398....

* Fibonacci, who lived in the 12th century, was a mathematician. During his journeys to Egypt he also discovered the mathematical relationship of the golden mean. The universal genius, Leonardo da Vinci, reflected the proportions of the golden mean in his divine creations. Plato saw in Phi a direct mathematical relationship with the cosmos.

If we take a look at the following mathematical curiosities associated with Phi, we may understand these scientists and philosophers and their admiration for this seemingly mystical number. By examining the length of an ancient Egyptian measure, the so-called Royal Cubit, one can recognize a close relationship that seems to exist between Pi and Phi.

It was always presumed that this cubit represents p /₆ of a meter (= 0.523599m). But as the calculations of the Great Pyramid will later show, it is actually Phi squared divided by 5; i.e. j ² /₅ = 0.523606m (j is the symbol for Phi).

This relationship becomes also evident when calculating the volume of a sphere:

Based on Pi the formula is d^{3 ´} p /₆ , but based on Phi it would be d^{3 ´} j ² /₅ . For instance, applying the formulas to a sphere that has a diameter of 1 meter, the difference amounts to about 8cm³. In other words, given a volume of 65 liters of water (e.g.) it comes down to a difference of only approx. 1cm³ - just a few drops more than the exact amount according to Pi.

Phi is also the only number that when subtracted from its square results in the integer 1:

Here are some more "unusual" equations that only work with Phi:

j ³ = 2j ² -1 = 2j +1 , j + ¹/j ² = 2 , j ² + ¹/j ² = 3 , (j + ¹/j )² = 5

According to Drawing 23, if we were to add r₁ and r₂ we would obtain a diameter of 2.11803398.... The result of multiplying this irrational number with p is a circle with a circumference of 6.6540000. This value lies between the other two circles. What seems uncommon is that the product of two irrational numbers results in another irrational number containing a sequence of zeros.

Almost mysterious appears to be the relationship between the three irrational numbers Pi, Phi and e*, given that j /p ´ e = 1.4000 - again, another irrational number that contains a sequence of zeros. It is not surprising that everywhere in Nature we can discover the logarithmic spiral based on the number Phi - the Evolution depends on it. The Dogon also speak of a spiral of a creation and of "seeds" continually being ejected from Sirius B.

* The number e = 2.71828.... is the basis of the natural logarithms and the exponential functions. Only with Pi is it possible to create a curved function producing an exact circle.

Finally, looking at Drawing 24, we can perhaps sense the perfect harmony of Phi as described by the equations

x² - x = 1 - y and x -¹/_x -1 = y

Maybe now we understand Plato and Leonardo da Vinci, who saw divinity in the golden mean - the hermetic rule.

The Calculations

With all that mathematical knowledge about Phi we are ready to analyze the oldest, largest and most exact building on Earth - the Great Pyramid. From the inside to the outside it is designed according to hermetic principles, although nowadays it is very difficult to realize this when looking at its heavily damaged facade. Unfortunately, the exact height can no longer be reconstructed due to the missing capstone. The same applies to the exact angle of inclination due to the missing limestone facade. The Great Pyramid must have looked magnificent when these fine and seamless casing stones were still in place. But these unique stones were used to rebuild Cairo's palaces and mosques after several major earthquakes hit the area around the 13th and 14th century. The only measure that one has been able to reconstruct fairly accurately is the length of the pyramid's base. It is said to be 230.38 m.

It is believed that this problem has been explained with Pi, since the relationship between the lengths of the pyramid's base (2b) and its height (h) can be expressed by the equation (2b) ÷ h @ ¹/₂ p. However, as indicated earlier, the accuracy is 99,9%.

The Great Pyramid can only possess a certain slope in order for Herodotus' statement to be true. Evidently, the calculation of this angle is based on the number Phi (see appendix below). We have three possibilities to compute the angle of inclination with Phi:

Knowing this important data of base length and slope it is no longer difficult to determine the exact height (h), which is obtained by multiplying half of the base (b) with Ö j. (see Drawing 25)

h = b ´ Ö j = 146.528...m

The Great Pyramid may indeed be called the "stone of wisdom". It is a symbol of the immortal hermetic wisdom and a sacred monument of the highest scientific achievement of an earlier, advanced civilization.

There does exist a real need for mankind to have its real history revealed.

"Egyptian civilisation was not a development, it was a legacy"

"Nachdem dieses sich also verhält, so ist in allen wesenden Dingen der Sinn, weil sie ohne denselben nicht können sein. Aber die Erkenntnis ist weit unterschieden von dem Sinn, denn der Sinn ist das Ende der Macht und die Erkenntnis das Ende der Wissenschaft, die Wissenschaft ist eine Gabe GOTTes." (XII. Buch 32-33, Hermetis Tris-Megisti)

We also know that the celstial position of Sirius relative to the Earth's equator is minus 16°40'25". Since the axis of the Earth has a fixed orientation between Sirius and our Sun, the position of Sirius relative to the equator does not change significantly except for some minor variations.

Now this would lead us to the mysterious "pyramid-forces", but that will be another subject and chapter. Suffice to say, if the so-called pyramid-effect does indeed exist, then it can only occur due to certain energies penetrating into the pyramid. One would think that in order to achieve optimum energy efficiency and/or resonance, the angle of refraction of the pyramid's material needs to be taken into consideration. Since the slope of the pyramid is 51.827°, the angle of elevation for Sirius with respect to the perpendicular to the pyramid's surface is 5.16° (see Drawing 27). Therefore, if "energies" emanating from Sirius were to pass through the pyramid at that angle, they would be deflected due to the refractive index (angle of refraction) of limestone, which is about 3°, resulting in a total deviation of approx. 2°. Consequently, from the rising to the setting of Sirius the Great Pyramid would be ideally "illuminated".

The astronomical fact that the southern 45° shaft is almost exactly aligned to Sirius during its culmination, may not be a coincidence. Yet this phenomenon, that the most revered star in Egyptian history shines directly over this shaft, only occurs every 25800 years according to the theory of lunisolar precession. Some experts, therefore, imagine that the designers of the Great Pyramid must have somehow planned for this rare cosmic occurrence so we can witness it during our lifetimes. Imagine - Just for us, who in the eyes of the ancient Egyptian priests are probably nothing more than the descendants of grave robbers.

Uwe & Karl-H. Homann

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Base of the Pyramid = 2b

Height of the Pyramid = h

Height of the Pyramid's side (triangle) = c

(Please, see also Drawing 26)

Solution for the assumption that the area of the side triangle is equal to the square of the height:

h² = c × b

h² = c² - b²

Þ c² - b² = c × b

In order to determine the relationship between c and b, let us assume that b = 1

Þ c² - 1 = c , or c² - c - 1 = 0

According to the solution for the general quadratic equation x² + px +q = 0

Þ x _1,2 = - ^p/₂ ± Ö ^p2/ ₄ - q

q.e.d.