mirrored file at http://SaturnianCosmology.Org/ For complete access to all the files of this collection see http://SaturnianCosmology.org/search.php ========================================================== ANDREW CONNER'S RESEARCH ______________________________________________________________ Analysis and Method for the Giza Great Pyramid Masonry Courses Part 1. Introduction: The Great Pyramid has probably been the most earnestly measured architectural structure ever to exist. As the last remaining wonder of the ancient world, it is remarkably un-interesting with regard to the recovery of tangible artefacts yet as a monument of megalithic proportions has sustained the interest of expert and amateur alike with a mystical alure to explain it's reason for existence and method of construction. Notwithstanding the internal passages and chambers, the limestone masonry courses as defining the external structure itself are and have been for generations the subject of measurement and continuous speculation. Individual courses were measured and the the results published by Piazzi Smyth¹ and subsequently by W. Flinders Petrie² both over a century ago. Smyth measured course heights and corresponding elevations above base to the nearest British inch which were published in tabular form. Petrie measured and recorded heights and elevations at geographic corners with decimal accuracy and presented the data in a graphical format utilising cumulative individual course heights. See [1]here for a standard reference to Petrie's data. Course Information: A general summary of course particulars is given in the following table:- Statistics of G.P. Masonry Courses Number of Courses Maximum Course Height Minimum Course Height Mean Course Height 203 58.6 19.7 26.851 Range Median Std.Deviation Variance 38.9 25.3 6.401 40.973 The course data can be represented as follows with cumulative heights against individual course heights. The vertical axis which represents elevation above base has been scaled at 100:1 and the axis labeled with the course numbers. [INLINE] It was noted by Petrie that thicker courses are located at certain levels above the pavement baseline and that the average course heights decreased with elevation. These observations have not been significantly expanded upon since. Mr Yashika Sue³ has more recently verified these general trends but has been unable to establish any mathematical patten. The course data envolope does however exhibit a somewhat serrated profile with a fractal-like apearance. This would suggest that there could in fact be an underlying algorithm within what outwardly appears to be a somewhat random choice of course heights. As an engineering project of such magnitude, it seems ludicrous that a standard dimension had not been chosen for masonary course heights. Multiples and fractions of which could be utilised within the scope of construction practices. The purpose of this article is to show that the ancient Egyptian architect/s had in fact an organised and pre-conceived scheme which dictated the thickness of masonry courses at specified elevations. Method Defined: Groups of masonry courses have been identified as belonging to specific sets. The example given below for set #4 exhibits a very accurate representation of the scheme. For the purpose of this method it should be noted that the elevation for a specific course number should be taken for that of the course directly below when reading from Petries's data. Petrie used the top of each course as a datum although it is valid that any given physical course, has both a top and bottom elevation. Key Courses - Data Sheet Set #4 [INLINE] Course No.s 155 114 77 42 Defining Angle 75.96 Degrees. Base Offset 31.5 Notes: 1. The sum of Course No.s = 55x7 +3 2. The defining angle is exactly arctan (4) 3. The common interval between courses is 1000. The initial course is 1400 above base. Other Courses: The following are given as additional examples however it should be stated that they are not intended to be interpreted as being complete. Key Course Sets Set ID Course Numbers Defining angle Base Offset #1 192 185 145 68.15º 40.92 #2 152 126 114 96 90.00º 23.00 #3 197 144 118 1 56.46º 58.60 #4 155 114 77 42 75.96º 31.50 #5 191 121 36 63.45º 47.03 #6 197 118 56.10º 59.08 #7 169 142 67.56º 40.00 #8 122 97 63 90.00º 26.00 #9 141 135 81.88º 26.81 #10 150 48 5 71.57º 40.87 #11 158 19 66.51º 41.00 #12 50 42 31 17 90.00º 28.00 Attributes 1: Sums of Course Numbers Set ID Sum of Course Numbers Nearest Multiple of 7 Error +/- #1 522 75 -3 #2 488 70 -2 #3 460 66 -2 #4 388 55 +3 #5 348 50 -2 #6 315 45 0 #7 311 44 +3 #8 282 40 +2 #9 276 39 +3 #10 203 29 0 #11 177 25 +2 #12 140 20 0 Attributes 2: Defining Angles Set ID Defining angle arctan of Defining Angle #1 68.15º 2.49 #2 90º inf. #3 56.46º 1.51 #4 75.96º 4.00 #5 63.45º 2.00 #6 56.10º 1.49 #7 67.56º 2.42 #8 90º inf. #9 81.88º 7.00 #10 71.57º 3.00 #11 66.51º 2.30 #12 90º inf. In Conclusion: 1. This article outlines the architect/s method which explains the profile of the masonry course diagram presented herein. 2. The implicit use of the numbers 5,7 and 11 should be noted. 3. Where tangent angles have been mentioned, these can be substituded with simple gradients. 4. The relationship between base offsets and key course intervals have not been included in this presentation. 5. By utilising different scaling factors similar relationships have been found to exist. References: 1. Piazzi Smyth - The Great Pyramid 2. W.M.Flinders Petrie - The Pyramids and Temples of Gizeh 3. Yoshiki Sue - http://www.mars.sphere.ne.jp/p-inpaku/Pyramid/Courses.htm ______________________________________________________________ Copyright © MMII Reproduction prohibited without written consent of the author. Eur.Ing. A.D.Conner B.Sc. C.Eng. M.R.I.N.A. [2]adconner at public1.sta.net.cn [3][LINK] References 1. http://members.optushome.com.au/fmetrol/photo/plate8b.html 2. mailto:adconner at public1.sta.net.cn 3. file://localhost/www/jnocook.net/saturn/files/giza/index.html