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Mathematical Facts About The Great Pyramid

Posted on Friday, 29 November 2013 by Pyramid Benny in Archaeology, Views: 15K, Reviews: 1




The Great Pyramid, photo taken by: Nina Aldin ThuneThe great pyramid at Giza is one of the seven wonders of the world and yet a lot of experts, egyptologists, archaeologists, and other researchers disagree on how it was built and, even more, what it's purpose is or was. Some speculate that it was a tomb. Others say it may have been some sort of power generator or astronomical device. Descriptions of Giza date back to fifth century BC during the time of Herodotus.(1) The point is that no one can agree. We need to look at the pyramid from a different approach, a mathematical approach, if we are going to make any sense of what the great pyramid has to offer.

There are mathematical underlines that are embedded into the structure and positioning of the great pyramid. Some are very simple to find, others not so much depending on your knowledge of mathematics. Some of these facts can be dated back to 1859 when a mathematician, John Taylor discovered that if one multiplies 2pi with the perimeter of the great pyramid it would equal the height of the the great pyramid.(2) His book was published in the same year and his work was later expanded upon by other researchers like Charles Piazzi Smyth.

Most of the casing stones covering the Great Pyramid were stolen in the 14th Century by Turks and Arabs to build homes and mosques. Some can still be seen at the top. Fortunately, one was shipped to England where it was scrutinized and verified for it's exact measurements, including the slope angle, which measured to 51.8539761 degrees. The Great Pyramid scholar Professor I.E.S. Edwards considered this to have been the 'normal' or most typical slope choice for pyramids as well.(12) This slope angle number is important to us because now that we have the slope angle of the great pyramid, we can use basic principles of geometry to verify this answer, just as John Taylor may have a few hundred years ago.


Giza Angle Dimmensions
Apex Angle 38.1460239°
Slope Angle 51.8539761°

Representation of The Great Pyramid's angles measured in degrees.
By simply drawing a 51° pyramid (more importantly 51.8539761°) and a straight 90° line from the very top of the apex to the bottom, to signify other sides, we can extract the number of degrees between the sides of the pyramid using basic principles from geometry. Remember, that in a triangle the three angles always add up to 180°. Thus, we simply use the dimensions of our 51.8539761° pyramid and then add our, 90° right angle, which we drew thru the top of the apex to the bottom signifying other sides. Now we can subtract this value from 180 degrees to leave us with 38.1460239° which is the number of degrees between the sides of the great pyramid!

Take the Tangent value from the apex angle that we just got (38.1460239°) and multiply it by the number of sides (4). TAN(38.1460239) = 0.785398175 × 4 = Π (3.14159265), pi. Just like John Taylor may have discovered hundreds of years ago, except now without all the controversy, and possible jailing.

Since we have already examined and confirmed the tangent value of the apex angle (38.1460239°), let's Let's take things another step further and examine relationship of the tangent value of the slope angle (51.8539761°). The tangent value of the slope angle, 51.8539761, is 1.27323952. Let us multiply that with pi3 and see what answer we get. Care to take a guess what the answer might be? You were right, pi again, rather a variation of pi. pi2 rather. 31.00627668 (Π3) × 1.27323952 (TAN Value of the Slope Angle) = 39.2784176 (Π2). The Great Pyramid is beginning to radiate pi.


The angle of a 51 degree pyramid comes into play again with geometry using Vesica piscis. Which is basically the relationship of two equal circles.(3) The Vesica picsis embeds a 51 degree pyramid within itself. If you were to draw two circles with the same radius intersecting in such a way that the center of each circle lies on the perimeter of the other and then nest that exact form inside itself, it becomes pregnant with a 51 degree pyramid as seen in the video. We also learn that the Yin and Yang Diagram of Taoism has certain “phi” relationships(3) and also form a 51 degree pyramid within itself and the Vesica picis.

The 51 degree pyramid is at the heart of squaring a circle. Mathematicians say that all circle and square constructions are approximations due to the transcendental nature of pi. We can investigate this by drawing a circle with the diameter of 9 around a square with the the edge length of 8. Both the circle and square's areas will be equal to within 99%. You can also do this comparing the lengths. They too will be equal to within 99%. Drawing a pyramid tangent to the circle we can discover that its slope angle will also be 51 degrees. The slope of The Louvre Pyramid in France also measures 51 degrees, but there is more to the 51 degree slope significance at the Louvre Pyramid. Scott Onstott confirms in his documentary(4) that the azimuth of the Louvre Pyramid during the summer solstice sunrise also measures from true north. Which is something that the Great Pyramid also incorporates. In-fact it's only only 3/60th of a degree of error. It is more accurate than the Meridian Building at the Greenwich Observatory in London, which of by 9/60ths of a degree.(5)(6)

Photo taken in 1940 of Giza taken during the summer solstice. The great pyramid also reveals that during the solstice the sides seem to cast a shadow effect to make the appearance of having eight sides instead of the four sides.(7) This was confirmed by accident in 1940, when a British Air Force pilot, P. Groves, was flying over the pyramid.(8) He happened to notice the concavity(9)(10) shadow effect and captured the now-famous photograph you will see to the right.

We do not have the conclusive evidence as to why the builders at Giza chose to incorporate this effect. The only answer we currently have is that they did this to signify the solstice. What we do know is that this effect was most certainly not incorporated by chance or mistake. From an engineering perspective, it most certainly would have been known to the builders and developed by choice, not by accident.

There are other megalithic structures that incorporate the solstice effect into their design. Most popularly, the Mayan Chichen Itza pyramid in the Yucatan Peninsula, Mexico. On the northwest corner of the pyramid it features a series of triangular shadows that evoke the appearance of a serpent wriggling down the staircase. Some scholars have suggested it is a representation of the feathered serpent god Kukulkan.(11) The isle in Gavr'inis France also orients its passage with the winter solstice(13) so that the sun can shine through. Similarly, Newgrange in Ireland also allows the sun to shine directly along the long passage into the main chamber when it rises on the winter solstice.(14)(15)


The Giza Pyramid Complex with an overlay of the Orion constellation. There are many more mathematical coincidences that can be explained and further investigated to better help unravel the mystery of the great pyramid, but one answer definetly remains certain: The Great Pyramid is most certainly more mathematically inclined than we can give ancient Egypt credit for. These facts speak for themselves, and really we are just touching the tip of the iceberg. The amount of geo-mathematical and astronomical coincidences they have to offer is quite extensive. Such as, the famous Orion correlation theory.(16) Needless to say there is more to be offered, more to be studied and analyzed.

Those who put a lid on these facts and label them as mere coincidences is the price we pay for the ignorance of that person's own self delusion. Whether they are a tenured professor, credited archeologist, or just a amateur student. These are the same people who probably think the Great Pyramid served as a tomb. This still has yet to be proven because no pharaohs, sarcophagi, or mummies have been recovered from the Great Pyramid.(17) If you want an answer to why the Great Pyramid exists, think about the importance it has already served and continues to serve and then you might find more of an answer and not some hidden mystery built up to scare or mislead. The great pyramid is there for all to see, all to learn. While we already know a lot about the Great Pyramid, there is more to unravel and make sense of its true meaning.




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Tickle reviewed on Tue, 05 Jan 2016 at 2:58 PM1 votes 

  • 5 out of 5 stars

this is really a good read. there's alot of good information here. how did you know about the tangent value of the slope angle being equal to PI? that's awesome!