INTRODUCTION

My interest and studies about the pyramids of Egypt came as a result of the continued and insistent manifestation, in my daily life activities, for many consecutive years, of the number 153. It was something unusual, outside statistical expectations. Continually and insistently I saw this number in ads, car license plates, magazines, in my engineer’s calculations, etc. I noticed this phenomenon even in my trips to different countries. I thought it was my lucky number, but I never have received a prize from it.

It is well known that the number 153 has unusual and strange characteristics. For example: In the Bible, Verse John 21:1, the third time Jesus showed himself to the disciples after the resurrection, was in the shore of the sea of Tiberias. Jesus showed up in the morning, after a night where the disciples were fishing and caught nothing. He oriented them to cast the net to the right side of the boat to find the fishes. After the disciples cast the net it was difficult to draw it out because of the multitude of fishes. The disciple Peter took the net to the presence of Jesus. It was full of big fishes, 153, and even with so many, the net was not broken.

Due to this passage, it is believed that the number 153 involves a religious message. This passage could have said that there were a great quantity of fishes... or many fishes... or that the net was full of fishes... etc. However, it was clearly specified that they were exactly 153 fishes.

From the mathematical point of view, the product of 9 multiplied by 17 is equal to 153, and the sum of the first seventeen whole numbers, that is, one plus two, plus three, plus four... etc., up to 17, is equal to 153. In another form, (1+2+3+4 ... +17) = 153.

Another interesting fact about the number 153 is that it represents the sum of its digits cubed. That is, the sum of one cubed, plus five cubed, plus three cubed, is equal to 153. Expressed in numbers, this would be (1)³ + (5)³ + (3 = 153.

From my own investigation, I found that the six combinations of its digits, 135, 153, 315, 351, 513 and 531, add up to 1998. All these numbers are divisible by 9. As a curiosity, I show in figure A, using a star figure, this numeric relation. It can also be observed, the relation between the number 153 and the number 666, also mentioned in the Bible, Rev 13:18, as the number of the "beast". The sum of 135 plus 531, 153 plus 513, and 315 and 351, all add up to 666. Although these numbers were of interest for me, my preoccupation was the insistent manifestation in my life of the number 153.

 

 

Figure A

I recall one day, about 30 years ago, in which I was interested in reading a book about the Great Pyramid. As a matter of fact, that day the number 153 appeared before me in several occasions. When reading the book, it called my attention that the Great Gallery has a length of 153 feet. There was the number again! Although that is not anything to preoccupy anybody, at that moment it did to me. To see the number again that day, overflowed the cup. I had to do something to find my relation to that number. It occurred to me that, maybe, I could find the answer if I continued my readings about the Pyramids. So, I decided to continue my studies. I acquired additional books about this topic.

In my studies, during a moment of meditation about the Great Pyramid’s construction, it came to my mind, that if I were the pharaoh’s engineer at those times, and he asked me to include the number 153 in his pyramid’s design, I would encoded the number in a formula, to establish its height. My understanding was that the pyramid’s height controls the design and was the most important dimension in the structure. In addition, I was supposed to trace the design using the figure of a circle. Therefore, I considered that I should combine in the formula, the number 153 and the circle’s identification. In order to do this, the height of the pyramid should be equivalent to the product of 153 (number required by the pharaoh) multiply by the value of Pi (p = 3.14159...) *. The value of Pi was used to indicate in the formula that the origin of the design was the figure of the circle. After my meditation, and motivated by my curiosity about this deep thought, I made the calculation. The product of (153) times (p) was equal to 480.66. I was really surprised... impressed... to find that this number was equivalent to the height of the Great Pyramid, expressed in feet, in accordance with my reference’s books. This means that the height (h) of the Great Pyramid has, as factors, the number 153 and p. I did not expect that. It was too much coincidence for me. I took it as a message to continue my readings about the pyramids. I also noticed that, since the circumference of a circle is equal to the product of its diameter multiplied by p, that is, C = D p, the circumference of a circle traced using the Grand Gallery’s length (153 feet) as its diameter, is equivalent to the pyramid’s height, (h) = C = (153) (p).

Using this equation, it can be stated that the ratio between the height of the pyramid and the length of the Grand Gallery is equivalent to p, that is, (153) p / (153) = p. These unexpected mathematical relations were extremely important for me. If they were known, I was sure that many reference books would emphasize them, since they add additional information of interest to the pyramid’s configuration. At least, the formula could be used to remember the dimensions of the height of the Great Pyramid, and the length of the Grand Gallery.

* The constant Pi is generally identify with the Greek letter p, and represents the ratio between the circumference of a circle and its diameter. The value of p is equivalent to 3.14159... and its decimal had been calculated billions of decimal places, without finding its end. Usually, its value is approximated to 3.1416.

I decided to investigate if this unusual and coincidental information was mentioned in other reference books available, especially those with esoteric doctrines and mathematical theories. I never found them explained in any book.

I continued my studies. I knew that in order to define a particular pyramid it must be known its height (and the unit of measurement), and the slope angle of the faces, or, the length of the base’s sides. Figure B, shows the usual configuration used to represent the concept of the Great Pyramid’s design using the figures of the circle, the square, and the triangle.

 

        

Figure B

The configuration suggested for the Great Pyramid’s geometry, as shown in figure B, is evident. The radius (R) of the circle represents the height of the pyramid. The triangle (HQT) identifies the cross sectional view of the pyramid, as seen through the center of the faces. The square between points I, II, III, and IV symbolize the pyramid’s base projection, as seen in the vertical plane. Nevertheless, in this configuration the slope of the faces, and the length of the sides of the base are not known. Therefore, and infinite number of pyramids can be designed using this concept.

In studies about the pyramid’s dimensions, it has been observed that the circumference of the circle having a radius equivalent to the pyramid’s height is equal (or almost equal) to the perimeter of its square base. Some investigators attribute this characteristic to a coincidence. Others believe the designers introduced it on purpose, and as a part of the pyramid’s design.

I started my search for a method or procedure to trace a geometric configuration to create the figures of a triangle and a square, where the triangle represents the cross sectional view have the pyramid, and the square the projection of its base in the vertical plane. In addition, my finished configuration should exhibit the same characteristic of similarity between the circumference of the circle and the perimeter of the base, as shown by the Great Pyramid. I wanted to develop it without the use of mathematical calculations and the use of any special drawing instruments. The radius of the circle represents the pyramid’s height. My drawing tools will consist of a straightedge, to draw the lines, and a drawing compass, to trace the circles.

After many, and long nights, tracing drawings, finally I developed the geometric configuration I was looking for, and the required sequence of steps to create it. My configuration also showed the very close relation between the circumference of the circle and the perimeter of the base of the pyramid. When I scaled the height of my pyramid’s model to 480.66 feet, I obtained angles, dimensions, and characteristics, equal to those shown in my reference books for the Great Pyramid. The results were so accurate that I was motivated to continue and to finish my work to define the whole structure. Finally, I established and evidenced my theory.

In 1982 I published my first book "La Gran Pirámide y su Geometría" (curiously, the book came out of press with 153 pages). In the book, I presented my theory that the geometrical design of the Great Pyramid had its origin in the figure of the circle.

After the publication of my first book, I continued my investigation on this matter, confirming and evidencing my theory with new findings. This, my second book on this topic, includes all my new findings and discoveries in this field. Many people will be surprised to know that the Great Pyramid’s design has such a simple origin, as I show in this book. However, I want to make clear, that with simple, I mean only the geometric pattern of the design, and not the complicated elaboration of its construction plans, or the monumental building of its structure. Students in Architecture, Mathematics, Geometry, Egyptology, and related sciences will find in this book a fertile ground to explore the Great Pyramid’s geometrical structure. So, I am sure that eventually, my theory will open its proper place in Egyptology.

The best way to present and demonstrate my theory is by presenting a geometrical exercise to create a pyramid’s model, independently from the dimensions and characteristics of the Great Pyramid, but finally, demonstrate that it has equal dimensions and characteristics, as those of the Great Pyramid’s structure. In other words, the Great Pyramid will be considered as nonexistent for the exercise purpose. After the geometrical design of the pyramid’s model is finished, a value will be established for its height. Since my design is based on a unitary circle (its radius symbolizes the pyramid’s height, and is made equal to one), the pyramid’s height can be of any value and of any unit of measurement. Each height’s value will produce a pyramid proportional in scale to the Great Pyramid. However, I found that it is when the height is set equal to 480.66 feet (the product of 153 multiply by p), that its angles, dimensions and characteristics, come to the exact scale dimensions as those of the Great Pyramid.

My idea about the criteria used by the Egyptian designers to build their pyramids includes two phases: first, to select from an infinite number of geometrical configurations, the one to be used for its design and construction. This phase does not specify quantities, or units of measurements. It only concerns the tracing of the pyramid’s geometrical structure, internal passages and chambers, and the underground work. The second phase consists of setting the pyramid’s height. This is the only measurement required. After the pyramid’s height is set, all other measurements will be automatically and proportionally set in the pyramid configuration.

I am sure that many enthusiasts in these matters, at the initial reading of this book will have doubts about finding in it the solution to the Great Pyramid’s design. Nevertheless, I am sure, that after reading the results of my studies, analysis and drawings; it will be very hard for them to believe that it is not. My theory is not related to science fiction, prophecies, predictions, or extraterrestrial. It is based on a simple geometrical process, easily for you to verify. You do not need to be an Egyptologist, a Scholar, or an expert about pyramids, to understand and verify them. The geometric exercise to create a design of a pyramid’s model, equal to the Great Pyramid, will be presented in the second chapter. The first chapter, for the readers’ benefit, contains general information about the Giza pyramidal complex and about the Great Pyramid.

It is my understanding that the important conditions to be satisfied between my designed plan and the Great Pyramid’s structural dimensions and characteristics are:

    1.  Both layouts must be in accordance.

   2.  The dimensions in both designs are within acceptable tolerances.

    3.  My designed plan could be used to explain unsolved

        conditions in the Great Pyramid.

     4.  My proposed geometrical method satisfies the design of

        other Egyptian pyramids.

All of these conditions are met in my theory, as it will be proven in the following chapters. We have to keep in mind that we are comparing data calculated from a designed plan, against data and measurements as taken from pyramid structures built five millenniums ago.

I do not know if my mission with the number 153 is finished. However, it continue its appearance in my daily life and has served me as a beacon during all the time I have dedicated to these studies. On my part, I am completely satisfied to present on these papers, the results of my extensive investigation about the Great Pyramid, "with my desire and expectation that it germinates as a mustard seed for all interested in the search for the truth".

 

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