THE HORIZON THEORY

THE HORIZON THE= ORY, PART-I

ORIGINAL CONCEP= T PLAN OF THE PYRAMIDS PLATEAU

Dr. Hossam M. K. Aboulfotouh*

1- Abstract:

= The paper shows the astronomical criteria that the designers of the Giza pyramids use= d in order to design the site plan of the three pyramids. It proves that the pyramids builders did study the daily motion of the sun during the year in their days, and based on their findings they set the positions of the three pyramids in the horizon of Giza plateau to encode three astronomical inform= ation concerning the daily motion of the sun on specific year: the meridian angle= on the vernal equinox, the meridian angle on the summer solstice and the sunri= se angle on the summer solstice. Accordingly, the encoded date of design of th= e Giza pyramids was= identified as 3055BC approximately, based on identifying the tilt of the earth's axis = (obliquity angle) in their days (24.10°) and counting the difference between it and that in our days (23.44°), in terms of years.=

Keywords: Giza pyramids – Pyramids Horizon – Egyptian astronomy – Archaeoastronomy

1- INTRODUCTION:

The horizon [1] theory[2] belongs to the ancient Egyptian architects who built the pyramids of Egypt a= lmost five millenniums ago. This research is the first step towards reviving it. = The theory deals with the pyramid's ideology, its design principles and its rel= ated knowledge and sciences. It depends on, and draws from, astronomical theories and cosmic sciences. It links time with space dimensions. The following paragraph is a modified version of the old story of the pyramids that was m= entioned in old golden plate that was found and translated during the days of King Philip (the father of Alexander), which was based on the dream of the King = Soraied[3]. It should be kept in mind while going through the present work.

The master priests or (Jedars)[4] of ancient Egypt discovered the mathematical law of the lifecycle of the celestial bodies, f= ive millenniums ago. They were able to determine then, based on their scientific knowledge = in basic sciences (mathematics, geometry, chemistry, physics, astronomy, etc.)= the timeframe of the frequent super-natural disasters of the earth. Their calculations had ensured the= m that the coming earth disaster will occur after four hundred years from their da= ys. Soon they decided to inform their King Soraied to establish a long-term pro= ject to save the accumulated scientific knowledge of the Egyptians for the new generations of the next cycle. They believed, as it was dominant in their d= ays that the normal people should not know this type of knowledge; hence, it should = not be recorded in a written form. They had decided instead, to record their ba= sics sciences in geometrical and numerical forms. The structures we define today= as "Giza pyramids" and its integrated-site are the hard disks within which all the laws of bas= ic sciences that were discovered and understood by Egyptian Jedars of t= he previous earth cycle had been recorded. These pyramids and its integrated-s= ite are the horizons of the earth knowledge. Perhaps the supreme objective [5] of the pyramids project encouraged all Egyptians to participate financially in their implementation. This story may be seen those of the nowadays' movies = of science fiction. In fact, the scientific proof of the whole story cannot be covered in a single research paper. The scientific findings of the present = work show the prelude to its full display.

Scientifically speaking, = this primary endeavor will show and translate, in words, mathematical formulas, = and geometrical diagrams, one of the coded messages (files) that are related to= the design of the Giza= pyramids plateau. It briefly describes the principles of its original design concept and how the designer planned it from an astronomical point of view. Besides, it aims to cor= rect the biased views, conceptions and information that were inserted in many books = of human history on the pyramids of Egypt. For example, first, some historians think that the pyramids architects did waste national resources to build nothing more than tombs. Second, some amateurs imagine wrongly that the pyramids builders were extraterrestrials. Third, the authors of books of th= e history of sciences declared that basic sciences in general, and astronomy in particular, were originated by the Babylonians and then improved by the Gre= eks; some have argued that the contribution of the ancient Egyptians in astronom= y was limited [6]. Fourth, there is disagreement between scientists and historians regarding t= he time when Giza pyramids were built.

This paper is structured = in three parts. The first part discuses the core issue of searching on the pyramids' design-principals. It follows the research technique of social sciences that draws its conclusion based on qualitative arguments. The seco= nd part is an attempt to retrieve the Egyptian priests' scenario for recording= the observed daily motion of the sun. It draws its conclusion based on establis= hing an array of logical and practical assumptions. The third part discuses the design principles of the horizon of the three pyramids in Giza plateau. It follows the research technique of basic sciences that draws its conclusion from facts and based = on mathematical proof.

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2- DEFINING THE CORE ISSUE:

The pyramids of Egypt w= ere the subject of scientific researches for many centuries. Many scientists and archaeologists focused on the three pyramids in Giza plateau. They were, and still are, trying to find answers for many questions, such as: (i) Why and how the Egy= ptian Kings built the pyramids? (ii) Why the designers used this geometrical form? (iv) What their measurement unit was? (v) Has it any relation to basic scie= nces like mathematics, physics and astronomy? (vi) What is the basic design conc= ept behind the alignments of the three Giza pyramids? During the last two decades, few researchers investigated the supposition that the designer of these pyramids and its site could have been scientists, who create designs based only on sound scientific theories and = not based on false imaginations, e.g. the web site of Giza Pyramids Association inclu= des many of these researches (www.gizapyramids.com). They were, how= ever, not able to find logical scientific answers within the frontier of science that, until then, were discovered by man. Thus, some have argued that they = might were aliens and accordingly the design theory of the pyramids still not fou= nd.

In fact, it is difficult = to use today's sciences to trace the design principles of architectonic artifa= cts that were designed with the aid of undocumented sciences. As time goes on, = the frontier of sciences gains newly discovered scientific theories and thus it expands. However, few of the new theories were effective when applied, for decades, in different circumstances. Besides, in the architectonic realm, p= eople always think that the new theories might achieve their welfare-dreams in mo= re effective ways, and thus old theories are usually forgotten if they were not documented. During the short lifetime of a person, in comparison to the lifetime of the humanity, one can hardly observe, in the architectonic fiel= d, the consequences of a complete shift-in-application from one theory to anot= her. For example, suppose that the universities of the world had stop teaching t= he design theories of the skeleton structures for a thousand years and taught instead other new theories, which are completely different and all the documents of the old theories were lost. Most likely, the civil engineers o= f the future generations will not be able to understand how the still-standing skeleton structures are structurally working, unless they find out how to retrieve the design theories that were used in their designs and implementations. Similar example is arising today, most of the civil engine= ers that were graduated, during the last three decades, at the universities of = many countries of the world know very little about the theories of masonry or be= aring-walls' structures. It was due to the shift from teaching the old theories of beari= ng-walls structures into teaching the nowadays theories of skeleton structures. Thus= , in the coming decades many countries will face the problem of lacking the loca= l expertise for restoring the structures of the masonry architectural heritage. In fact, one could argue that similar shifts were occurred in other fields of scienc= es too.

The above may answer the question: why today's engineers can hardly find the lifting techniques that were used to construct the ancient megalithic structures? The scientific papyri that describe these techniques were not found in Egypt or elsewhere. The histo= rians[7] did mention few general stories on this subject. Thus, today's scientists are trying to discover these ancient techniques; some believed that the ancient architects were using some sort of anti-gravity systems in order to lift the large stones. Besides, as mentioned earlier, many endeavors have been made towards understanding the basic concept of the pyramids design. The world-w= ide-web includes hundreds of researches and articles on these subjects and that man= y of them are related to Egyptian pyramids; however, until now nobody did find a= solid scientific [8] conclusion for any of the two architectural issues in hand, namely: the pyramids' construction techniques and the pyramids' design principles.

Today, in the industrial field, the term "reverse-engineering" means retrieving the knowle= dge behind the design concept and the production process of such machine of a k= nown function and that was produced by others. Similarly, the architects have us= ed to retrieve the design principles of such ancient building of a known funct= ion. In both cases, the researchers do succeed in these processes because they k= now the functional-objective of the machine or the building under consideration. Concerning the pyramids, the problem is completely different; the keen rese= archers cannot easily decide about what was their functional objective. In this cas= e, therefore, the retrieval process should primarily focus on the educational paradigm of= the ancient Egyptian architects (priests) in order to discover the knowledge be= hind the designing of the pyramids and their integrated-site. The Arabian histor= ians[9] during the medieval eras said that, "the pyramids designs were based on excellent astronomical knowledge." However, none of the nowadays archi= tects have tested this postulation, i.e., is it correct that they have used the astronomical knowledge as architectural-design-principles, and interpreted = it into the architectural language. Accordingly, the core issue of the retriev= al process is to find out, how had the architects of the Giza pyramids plateau learned the basic= astronomical knowledge and interpreted it into architectural designs.

3- THE SCENARIO OF ASSUMPTIONS: THE SUN A= S A SOURCE OF ASTRONOMICAL KNOWLEDGE.

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To date, Egyptologists did not find any scientific papyrus[10] on the ancient Egyptian astronomy. Today's scientists, therefore, believe t= hat the contributions of the ancient Egyptians in this field were limited. Although= the design of the temple of Abu-Simple and t= he diagram of constellations (zodiac} of Denderah temple lack the astro-mathem= atical formulas that support their perfect designs, today's scientists consider th= em as products of skilled astronomers. However, some astronomers believe that = the latter was designed during the Hellenistic period [11]. On the other hand, other than the false assumption of adjusting the tilt of the great pyramid's entrance-passage to point to the North-Star, or aligning the pyramids [12], Giza py= ramids in general have no other signs in relation to spherical astronomy that coul= d be noticed by normal observation. Besides, using the modern astronomical theor= ies to analyze the pyramids design concept is an imperfect methodology. This is because the researchers, in this case, presume that the pyramids architects= were thinking like the astronomers of today. In addition, researchers can hardly= trace the advancements in astronomy during the three millenniums before the days = of Pythagoras (approximately 550BC). They will stack with the problem of defin= ing which theory was discovered first.

Therefore, this part of t= he paper is an attempt to retrieve some astronomical principles that might have been used in the design of the horizon of the three pyramids in Giza plateau. This retrieval process will be based on establishing a hierarchy of basic-assump= tions that together might form a logical scenario. The validity of that scenario = will be tested quantitatively, by linking its likely accumulated knowledge with = the geometric survey data of the site-plan of the three pyramids in Giza plateau.

As a point of departure, assume that Giza pyramids were the outputs of ideal-thoughts of architects who studied not o= nly some sort of architectural curriculum[13] but also the basic astronomy. Then, a question might be asked: how to retri= eve their scenario of searching on basic astronomy? Of course, the retrieval attempt should be supported by both the basic information and the documented history of spherical astronomy [14]. However, this basic information should be kept in mind to be only a scienti= fic reference for guiding the retrieval process without affecting the logical hierarchy of the flow of knowledge to the ancient Egyptian architects.

Logically, their original source of astronomical knowledge should be defined first, presuming that th= ey were working only during the daytime [15]. Without doubt, in their days, the = sun was the only possible source of astronomical knowledge during the daytime. Then, one more questions should be asked: how they extracted information fr= om its observed but indirect daily motion [16], with the use of primitive tools? Probably, their scenario was based on recording, in each day of the year, the changes in both positions and lengt= hs of the shadow of a vertical post that was standing on a leveled ground. It = is known today that, the observed daily motion of the sun has an array of two basic-values that were, and still are, used in the field of architecture. The first is the value of the daily horizontal angle of sunrise [17] (or sunset) that architects have used to measure it from the east (or west) coordinate-direction of the place. The second is the value of the daily vertical angle of the sun, when the sun meets, or being at, the meridian of= the place [18]. Their scenario for measuring and recording these angles, during the daytime, might was consist of four steps, presuming that they were able to put tasks= in order. Firstly, marking on a leveled site [19] that its perimeter was circular in shape, and that was a small horizon-model similar to the natural observed horizon, the frequent positions of the end = of the shadow of a vertical-post (like an obelisk) that was standing at its center. Secondly, the identification of the two-coordinates of the place by following the method that will be mentioned in the next paragraph. Thirdly,= measuring and recording the values of the horizontal-angles of sunrises and sunsets. Fourthly, measuring and recording the values of the sun's vertical angles, = when the sun was meeting, or being at, the meridian of the place, as shown in figure-1 & figure-2.

Figure-1: The vertical angles of the Sun, when it meet= s or being at, the meridian of the place. The angles, from left to right, (S) = belongs to the summer solstice, (V) to the vernal equinox and (W) to the winter s= olstice (looking towards the west); (X) is earth's obliquity angle

Figure-2: A horizon's plan shows the horizontal angles of sunrises f ; from top to bottom, on su= mmer solstice and on winter solstice. Between these two extremes, the sun goes back and forth during the year, having a specific sunrise angle for each = day of the year.

Most likely, they were identifying the true geographic north [20] at any place, by using the shadow of a vertical post (like obelisk). In fac= t, the daily process of marking the end of the shadow of the vertical post dra= ws, an extrovert or introvert, semi-hyperbolic curve on a leveled ground; takin= g into consideration that each day of the year has a specific curve. The true geographic north-south axis might have been identified then as the line that divided, into equal parts, the angle between any two shadow-lines of equal length that were measured from the vertical post (obelisk) to the marked cu= rve, as shown in figure-3.

<= span style=3D'font-size:11.0pt;mso-bidi-font-size:13.0pt'>

<= span style=3D'font-size:10.0pt;font-family:Arial'>Figure-3: Identification &= nbsp; of the true geographic north.

If they were doing the ab= ove four steps for years, they might have established an array of yearly records that could be compared in order to draw-out additional results and conclusi= ons, presuming also that they were knew how to do comparative analysis. Then, if= they were well versed, they might have recognized that those angles were changing every year. Based on the nowadays' astronomical knowledge, sunrise or sunset angles of both summer and winter solstices are decreasing, the meridian ang= le of winter solstice is increasing and the meridian angle of the summer solst= ice is decreasing. However, in their days, they could have noticed the accumula= ted sum of yearly changes only after several decades. Concerning the meridian a= ngle on winter solstice, at the latitude of 30°, the shadow of a 20m-height post (or obelisk) would be increased by almost one centimeter af= ter 75 years. They might have noticed too that the sun was rising from the exact east-direction and was setting to the exact west-direction in only two days= of the year, which are known today as the two days of the equinoxes.

Concerning the calculatio= ns, suppose that they were untaught about calculating the value of angle [21]. No doubt, they could have got the same results by using only the trigonomet= ric ratio of the tangent. The array of tangent ratios would have been enough in order to get the similar hierarchy of relative values, as in the case of us= ing the values of angles. The discovered mathematical papyri [22] of the ancient Egyptians show that, during the new kingdom, they were able = to get the breakdown of any ratio, which was the base for comparing fractions = of numbers, similar to the nowadays system of comparing decimal numbers. Howev= er, the architecture of that period was not as sophisticated as that of the pyr= amids and thus, the mathematics during the old kingdom must was better or at least equivalent to that of the new kingdom.

Moreover, while they were comparing their results, they might have noticed too that, in each year, th= ere are days that have the same values of sunrise angles. If that had happen, t= hen it is likely that they discovered the fact that the sunrise angles of many = days during winter (and spring) were equal to the sunrise angles of other days during autumn (and summer); and the order of this array of two matching day= s (the twins days) was not changing. Then, if they were numbering their days that might were starting from the moment of sunrise and began with the sunrise of the vernal equinox (March 21), they might have established a table of daily sunrise-orientations. The original orientation of the axis of the temple of Abu-Simple, before its relocation, proves that its architect knew that the sunrise angle of the day number 215 (October 21) was precisely matching the sunrise angle of the day number 338 (February 21). It is ridiculous that the astronomical scientists who superv= ised the relocation project of that marvelous temple during the sixties of the l= ast century, were not able to conserve the prime astronomical orientation of th= at temple, and made unforgivable mistake by changing the dates to October 22 and February 22 with a = shift of two days, i.e., October 22 is the twin of February 20, and October 20 is= the twin of February 22.

Furthermore, if they were doing the same experiment at other places in the Delta and along the river = Nile and were comparing the data of these places, t= hey might have noticed two facts concerning the value of the meridian angle of = the sun during the equinoxes. Fir= st, it was changing as they moved along the south-north direction. Second, it was = not changing as they moved along the east-west direction. If this supposition w= as correct, then they might have used this fact to establish a system of east-= west geographic axes or latitudes [23]. However, it should be taken into consideration that if they were untaught a= bout that the earth is spherical in shape, and then their east-west geographic a= xes might have been named after the values of the meridian angle of the sun dur= ing the vernal equinox. Their number for the latitude of Giza plateau might was 60°; today's astronomers are using its complementing value 30°.

Likewise, if they were comparing the values of the meridian angles of the sun during the summer solstice, during the winter solstice and during the vernal equinox, they mi= ght have noticed other fact. That is, the value of the meridian angle during the vernal equinox was always the median between the values of the two extremes= , during winter and summer solstices. To explain this based on the nowadays' astronomical information, the meridian angle of the sun during the summer solstice is equal to its value during the vernal (or autumnal) equinox plus= the value of the obliquity [24] angle of the earth. The astronomers of these days said [25] that "the obliquity of the earth oscillates between 24.30° & 21.91= ° within a period of forty thousand years (twenty thousand years each way); i= ts current value is 23.44° approximately, in the descending path, which di= minishes by 0.47 arc-second per-year." Accordingly, today, in Cairo the meridian angle of the sun dur= ing the summer solstice has a value of 83.44° approximately (eq= ual to 60= ° plus 23.44= °). On the contrary, the meridian angle of the sun during the winter solstice is equal to its value during the vernal equinox minus the obliquity angle of t= he earth. Accordingly, today, in = Cairo the meridian angle during the winter solstice has a value of 36.56° approximately (equal to 60° minus 23.44°).

Based on the results that were concluded through doing the previous experiments, they might have also known how to measure the time and define the year. Apparently, they defined their year as a cycle that contains 365 sunrises. It may was starting at the sunrise of the vernal equinox. In addition, probably, they used the values = of the meridian angles of the sun during the summer solstices as a tool in order to record specific moment in their history.

To conclude this part, the above scenario of assumptions shows that the ancient Egyptian architects, priests and Jedars, could have been able to know the basic astronomi= cal knowledge via recording the observed daily motion of the sun, using the pri= mitive tools. The third part of this research is an attempt to prove that they used this knowledge as design-principles in order to formulate the contents of t= he first coded file in the horizon of the three pyramids in Giza plateau.

4- ORIGINAL CONCEPT PLAN OF THE PYRAMIDS PLATEAU:

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It was assumed earlier th= at the Giza pyramids and its integrated-site are the hard disk within which all the law= s of basic sciences of the previous earth cycle were recorded. Some may argue th= at this postulation is illogic. In fact, a similar example is quite well known today. During the twentieth century, computer scientists had invented the binary codes that enabled modern societies, among other useful uses, to rec= ord many forms of data (text, graphics, sounds, etc.) on computer disks. However, those who know nothing ab= out computers might not be able to recognize the value of a compact disk that contains, for example, the Encyclopedia Britannica (or Americana). They may see it as only a f= ine piece of plastic/metal. Similarly, = some may see the pyramids as only hills or pieces of stones. On the contrary, one could argue that, the designer of the Giza pyramids and its integrated-site did the same thing; he might have used spe= cial numerical and geometrical codes to record his knowledge, e.g., the encyclop= edia of the ancient sciences. The analyses of this part of the paper will be based on the presupposition that= the Giza py= ramids' designer used the horizon model of two-dimensions.

&nbs= p;

As a background-informati= on, the horizon of Giza= pyramids includes seven basic elements, which are the three pyramids, the Sphinx, the causeway and two temples. Its design concept included files of coded messages; they describe some of the basic theories on spherical astro= nomy and mathematical sciences of the Egyptian Jedars of the old kingdom. Here b= elow is the translation of one of these files on "basic astronomy," wh= ich forms the main design concept of the horizon of the three pyramids in Giza plateau. It = was based on the horizon's model that has been discussed earlier. This file included the idea of the alig= nments of the three pyramids, based on the knowledge that were extracted only from= the observed daily motion of the sun, and which accordingly defines the encoded= date of design or implementation of Giza pyramids.

Based on studying the exa= ct locations of the three pyramids and the sphinx, using the survey maps and t= he published results of Petrie's survey [26], it was found that the site plan of the Giza pyramids forms a horizon model that stands in a plane of two-dimensions. The center of this horizon is the point of intersection between the north-south axis of the great pyramid and the east-west axis of the Sphinx; they are the main two axes of the horizon of Giza pyramids. Through long process of trial and error, the radius of this horiz= on was found 746m. Figure-4 shows the basic concept-plan that followed the recorded data of the daily motion of the sun in their days, presuming that = an imaginary vertical post (or obelisk) of 746m height was standing at the cen= ter of that horizon in their days, as shown in figure-5. The following discuses the geometr= ical alignment of the three pyramids in relation to the observed daily motion of= the sun.

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Figure-4: The Original concept plan of the horizon of the three pyramids in Giza plateau<= /o:p>

Figure-5: A perspective shows the three basic information of the horizon: the meridian angle on the vernal equinox, the meridian angle on the summer solstice and = the sunrise angle on the summer solstice

First, the center of the great pyramid followed the meridian angle of the sun on the vernal equinox = (qv), at the end of the obelisk's shadow. Therefore, the location of the great pyramid (or its center) was identified to link the horizon with the latitud= e of the place, or to identify the latitude to which the horizon was linked. Thereupon, the distance from its center to the center of the horizon (L1) c= ould be identified as follows:

&nb= sp;

qv =3D 60= °

L1=3D 74= 6 / (Tan = qv)

L1=3D 43= 0.70m

Second, the center of the second pyramid followed the meridian angle of the sun on the summer solstic= e (qs), at the end of the obelisk's shadow in their days. Therefore, the location of the second pyramid (or its center) defines the exact date of implementation= of the horizon. The north to south distance from its center to the east-west a= xis of the horizon (L2) defines the obliquity angle of the earth in the year of implementation of the horizon, and its basic architectural elements. Howeve= r, the east-west alignment of this pyramid followed the astronomical knowledge= of another encoded file, which is out of the scope of this research. Thereupon, the distance (L2) and the implementation date could be identified as follow= s:

Tan qs=3D 746 / L2

L2=3D 77= .09m (it was measured from a survey map and corrected through trial and error)

Tan qs =3D746 / 77.09 =3D 9.6767

qs =3D 84.1= ° approximately.

qs =3D 60= ° + Obliquity angle in the year of implementation (or the encoded design date= ).

Obliquity angle in the year of implementation =3D 84.1° - 60° =3D 24.1= ° approximately.

Today's obliquity angle =3D 23.44° approximately.

The difference between obliquity values =3D 24.1°- 23.44°=3D 0.66= ° approximately.

The diminishing value of the earth's obliquity per year =3D 0.47 arc-second.

Total difference in years =3D (0.66° * 60 * 60) / 0.47 =3D 5055 years approximately.

Then, the date of design/implementation was 3053 BC approximately.

Third, the center of the third pyramid followed the sunrise angle of the summer solstice (f) in the year of design/implementation of the horizon. By calculation, the value= of this angle was found 28.13° approximately. The author has developed the following formula in order to identify the value of this angle [27]; it should be measured from the east coordinate of the place.

Sine sun= rise angle on summer solstice =3D Sine obliquity angle /= Cosine latitude angle

Sin. = f =3D Sin. 24.1= ° / Cos. 30= °; &= nbsp; then, = f =3D 28.13= ° approximately

The center of the third pyramid was placed on the intersection between the shadow of the imaginary obelisk and the east-west chord that defined the maximum obliquity angle of= the earth, which has a value of 24.30°; since the plan of the horizon is like a rotated cross-section in a spherical coordinate system where its center represents = the earth, i.e., the center of that system. That shadow occurred at the moment-of-sunrise, on the summer solstice of the year of implementation of = the horizon. So, the north to south distance (L3) from center of the third pyra= mid to the horizon's main east-west axis could be identified as follows:

&nb= sp;

L3 =3D 7= 46 * Sin 24.30= °

L3 =3D 306.989m

In addition, the east to = west axial distance (E3) from center of the third pyramid, to the north-south ax= is of the horizon, and the great pyramid, could be identified as follows:

E3 =3D L= 3 / Tan 28.13= °

E3 =3D 306.989 / 0.53462

E3 =3D 574.21m

&nb= sp;

Fourth, table-1 compares = the results of the survey that was carried out by Petrie in 1883 [28] and the results of the above calculations, which shows very minor differenc= es.

Table-1: Comparison between the Petrie's surveys = data and the results of calculations

Ranges of distances	Petrie 's survey data, = 1883	The results of Calculat= ions
North to south axial distance from center of the great pyramid to center of the second pyramid<= /p>	353.86m * (13931.6 inches)	353.41m (L1- L2)
North to south axial distance from center of the second pyramid to center of the third pyramid	385.32m (15170.0 inches)	384.08m (L2+L3)
East to west axial distances from center of the great pyramid to center of the third pyramid	574.44m (22616.0 inches)	574.21m (E3)

* (One inch =3D 0.0254 meter)<= /p>

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5- CONCLUSION:

The present work extracted and attempted to explain the first, and possibly the simplest, file in the concept plan of the horizon of the three pyramids in = Giza plateau. Apparently, the horizon, including its basic architectural elements, was one project; however, the implementation of these elements might have lasted for several decades. No doubt, its designer was a knowledge-based architect, who creates architectu= ral concepts based only on scientific theories. Although, the ancient Egyptians have used primitive tools in their researches in basic astronomy, perhaps, = they were able to establish a complete picture on spherical astronomy, i.e., the horizon theory of multi-dimensions. The introductory part of that scientific reference has been discusse= d in this work. The most interesting result that was found in this attempt was t= hat the ancient Egyptians knew the maximum obliquity angle of the earth. This means that, at the time of implementation of Giza pyramids, the Egyptian astronomical records were including the data of at l= east 1500 years. May be they were able to calculate its correct value. In the field of mathematics, the alignments of the three pyramids prove that ancient Egyptians were able to calculate the value of angles; or at least, they were using the trigonometr= ic ratios of the tangents.

Moreover, the horizon's concept should be taken into consideration when formulating and implementin= g the conservation projects for Giza= pyramids plateau as well as in the future processes of excavations within t= he plateau. Besides, the above s= hould support the view that it is highly unlikely to find a room of records insid= e or outside the pyramids. The scientific and holistic knowledge of the ancient Egyptians was recorded in = the concept design of their pyramids and its horizons.

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6- REFERENCES:

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

- 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-Tahr= ier, Bulaque Edition, Cairo, 1849.

- Al-Masoudi, Mrog = Al-Zahab Wa Ma'waten Al-Gawher (The Golden Lavas and the Metals of Essence), Asr= ia Library press, Saida, 1987.

- Carlo Nallino, Arabian Astronomy: its History During the Medieval Times, Oriental papers for publications, second edition in Arabic, Beirut, 1993. (1st edition, 1911)

- Selvie Cauville, Le Zodiaque d'Osiris, Louvian, pp11-13, 1997.

- Ernst Neufert, Architects' Data, English edition, Crosby Lockwood Staples, London, 1975.

- Gorg Serton, History of Science, Arabic edition, Ibrahim Biomy translator, Dar Al-Maaref, Cairo, 1957.

- Herodotus, History of Herodotus, Arabic edition, Abdel Elah Al-Mal= ah translator, Al-Magma Al-Saquafie, UAE, 2001, p.190.

- Jahon Whttow, Dictionary of Physical Geography, 1994.

- John McLeish, Number from Ancient Civilizations to the Computer, <= st1:place w:st=3D"on">London, 1992.

- Kate Spence, Ancient Egyptian Chronology and Astronomical Orientat= ion of Pyramids, Nature, Vol. 408, pp 320-324, 2000.

- Mark Lehner, Some Observations on the Layout of Khufu and Khafre Pyramids, Journal of the Amirican Research Center in Egypt, Volume XX, Egyp= t, 1983.

- Olaf Pedersen, Early Physics and Astronomy, a Historical Introduct= ion, Cambridge University press, New York, 1993.

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

- Webester, Webester's Seventh New Collegiate Dictionary, G & C. Merriam Company, publishers, USA, 1965.

7- GENERAL REFERENCES:

- Bernadette Menu, Pe= tit Lexique de l' Egyptien Hieroglyphique, a l' usage des Dedutants, librairie orientaliste Paul Geuthner,S. A., Paris,&n= bsp; 1989. (Arabic edition, Maher Guaygaty translator, Dar Al-Feker Publisher, Cairo, 1999)

- E. A. Wallis Budge, The Egyptian book of the dead: The Papyrus of = Ani, Dover publications, inc., New York, 1967.

- E. A. Wallis Budge, Egyptian Language: Easy Lessons in Egyptian Hieroglyphics, Egyptian International Data Bank Publishing Department, Cairo, 1910.

- Edwards I. E. S, The Pyramids of Egypt, rev. ed., Pitman, 1961= .

- R. I. Forbes & E.J. Dijksterhuis, History of Science and Technology, Arabic edition, Osama Al-Khuly translator, Family Library, Cair= o, 1999.

- Selim Hassan, Encyclopedia of Ancient Egypt, Vols. 1-18, Family Library, Ca= iro, 2000.

- Selim Hassan, Sphinx, Family Library, Cairo, 1999.