Great-pyramid-S3-pyramidal-form

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ARCHITECTONICS

From Cosmic Theories to Urban Development

Dr. Hossam Aboulfotouh

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THE HORIZON THEORY, PART-II: Internal Design Concept of the Great Pyramid.

Hossam Aboulfotouh, Ph.D

Assistant Professor, Department of Architecture, Faculty of Fine Arts, Minia University, and Director UIA-WPAHR-V fotouh@mail.com

[Proceedings of the German-Egyptian Conference on Conservation and Restoration, Faculty of Fine Arts, Minia University, 17-18 March 2005]

Section-3: The pyramidal form and the spherical system of coordinates

As said earlier, it has been proven architectonically that the pyramid of four sides is the geometrical form of the initial state of the evolution of our solar system; i.e., a pyramid of four sides is the geometrical cosmic form that represents our solar system. The spherical representation of that notation is that a pyramid is being put inside a sphere, where both the sphere and the pyramid inside it are having the same center that represents our sun. When interpreting that pyramidal-spherical system into the diagrammatic system of coordinates as described in section-2, the cross-sectional diagram on the latitude of 30° north will be as shown in figure-6. Again, in this diagram the Earth instead of the Sun is the center of it. The angle between the line Xw-Xe that represents the plane of the Earth's equator and the line h-h that represents the horizon of where the observer stands will be 60°, which complements the latitude angle of 30°. The line A-A represents the direction of the azimuth of the observer, which is perpendicular on the horizon line h-h.

In this diagram, the upper part of the pyramid appears above the horizon line h-h and its bottom part appears below it. The height T of its upper part and the height B of its bottom part depends on where exactly the center of the pyramid takes place, which accordingly identify the exact location of the pyramid within its spherical domain. That center represents the core of the basic system "Bs4" in Cs₂₄₊₄ (as previously shown in figure-2); thus, the plane of Bs4 is located at the level of that center.

Click on picture to see high resolution

Figure-6: The cross-sectional diagram of the astronomical coordinates that upon which the Great pyramid has been designed.

Now, suppose that the line P1-P2 is the diagonal of such rectangular P1-C-P2-D, wherein the north-south cross-section of the pyramid will be plotted. The width of the rectangular equals 2T, or twice the height of the upper part of the pyramid. Since the line P1-P2 represents the ecliptic plane of the imaginary yearly motion of the sun around the Earth, point P1 identifies the location of the sun at noontime in the day of winter solstice; it identifies the minimum meridian angle M of the Sun at noon of that day. Taking into consideration that the obliquity angle q at the time of erecting Giza pyramids was 24.10° and the latitude angle of the place is 30° , then this minimum meridian angel is given by,

M = 90° - 30° - 24.10° = 35.90° .

Accordingly, if R is the radius of the pyramid's sphere then,

T = R * Sin M (1)

Based on the author's analysis, it is found that the radius of the pyramid's sphere is the radius of the circle that passes by the corners of the square of the pyramid's base. It means that R equals half the diagonal of the pyramid's base. The value of R is such an assumption by the pyramid's designer. Besides, the author has been formulated the tectonic mathematical formulas of the law of the music of the spheres in previous study7. Based on that law, it is found that the pyramids' designer were using for the pyramids' spherical radii, only the numbers that indicate the twelve half tones of the musical octave. Thanking into consideration, the author's numeric analyses on the pyramids' dimension hints to that the designer was using the natural measurement unit that we call today a meter, which divides the north-south distance between two succeeding latitudes.

One may summarize the law of the music of the spheres in the coming few sentences. The imaginary frequency of the musical mote of any radius in meter value is the fourth root of that radius divided by the fourth root of 24, and multiplying the result by one hundred. For example, as shown figure-1, the author proved in part-I that the radius of the horizon of the site plan of Giza pyramids plateau equals 746m that indicates a musical note close to La-major of 234 cycles, which matches the musical note of the radius of Jupiter's orbit. However, the unit value for the radii of planets' orbits is million kilometers.

The lion body of the Sphinx indicates the ancient Egyptian letter L that denotes the musical note of La-major. For the great pyramid, the designer had set its R equals to 162.88m that implies a musical note close to Me, and he set its height equal to 146.5m that has a musical note Me-Re, which matches the musical note of the radius of the Earth's orbit.

Further, the analysis has shown that the designer set the ratio between the radius R of the great pyramid's sphere and its height equals to the ratio between the minimum obliquity angle of the Earth (21.673°) and its identified value at the time of erecting the pyramids (24.1°). If we take into consideration, that the designer was planning too to coding the ratio p =3.14 in his design, then he must have chosen first the value of the pyramid's height that has the accurate musical note Me-Re, i.e., the radius R of its sphere was a product.

Accordingly, from Eq.1, T of the great pyramid is equal to 95.50m. Knowing that the design height of the pyramid is 146.5m, then, the location of the astronomical center (core of Bs4) of the great pyramid is at 51.0m form its ground level, which equals to the vertical height of its bottom part B below the horizon line h-h in the diagram. Accordingly, the horizon line h-h represents, or takes place at, the level of the highest point of the grand gallery, or very close to it. Then the remaining of the bottom half of the rectangular P1-C-P2-D will appear as a base for the pyramid. In this diagram, the north-south cross-section of the pyramid and its base indicates the pyramidal symbol that appears in the ancient Egyptian texts .

Section-1: Introduction

Section-2: The astronomical Coordinate System of the ancient Egyptians

Section-3: The pyramidal form and the spherical system of coord.

Section-4: Great pyramid's shafts and entry passage, and its spherical domain

References:

1- Edwards I. E. S, The Pyramids of Egypt, rev. ed., Pit-man, 1961.

2- Farouk- El-Baz, Gifts of the Desert, archaeology Magazine, Volume 54 Number 2, March/April 2001

3- Encyclopedia Americana, Vol. 23, Grolier Ltd., Canada, 1978

4- Fathy Al-Bedawy, Pyramid and Computer: the symbol of Ancient and Modern Civilization, Cairo, 1991.

5- Aboulfotouh, H.: The Horizon Theory, Part-I: Original Concept Plan of the Pyramids Plateau, Cairo, proceedings of the UIA-WPAR-V International Conference, Bibliotheca Alexandrina, 2002. Www.fotouh.netfirms.com/horizon-theory-introduction.htm

6- Petrie, W.M.F., The Pyramids and Temples of Gizeh, London, 1883.

7- Aboulfotouh, H.: Determining Planetary Spin and Musical Gravitation in the Spheres of Cosmic Systems of Perfect Numbers, Cairo, Dar Al-Kutub, 2004. www.fotouh.netfirms.com/spin-gravity-introduction.htm

8- Al-Maqrizie, Al Mawaes Wal A'atebar Bezeker Al-khetat Wal Asar (Sermons and Lessons with the Discourse on Alleys and Monuments), Vol.I, Dar Al-Tahrier, Bulaque Edition, Cairo, 1849.

9- Al-Masoudy, Mrog Al-Zahab Wa Ma'aten Al-Gawher (Golden Lava and Metals of Essence), Asria Library press, Saida, 1987.

10- Plato, Timaeus, (330 BC.).part1-paragraph-6 http://psychclassics.yorku.ca/Plato/Timaeus

11- Olaf Pedersen, Early Physics and Astronomy, a Historical Introduction, Cambridge University press, New York, 1993.

12- A. Weigert & H. Zimmermann, Encyclopedia of Astronomy, Arabic edition, Abdelkawy Aiad translator, The Egyptian General Organization for Book, Cairo, 1990.

13- R. Gantenbrink in R. Stadelmann, MDAIK 50 (1994), 285-294. http://www.cheops.org

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