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# The Side Deviations

### THE FOURTH DYNASTY - GREAT PYRAMIDS OF EGYPTPART TWO

Copyright 2001, by Ernest P. Moyer
Revised February, 2003

My sources are the same as given in Part I above. Refer to References at end of last Part.

The data provide other information, clearly indicated on Figure One. The individual side orientations of Meydum differ from one another as much as 18'. The Bent enclosure wall has a scatter of 11', while Giza II has 1' 52" maximum difference among the sides. The Giza I core is within 1' and the case within 37" (Petrie). (For 3' 33" value by Cole see discussion below.)

These differences in orientation are related directly to differences in side lengths. A larger deviation from the true geographical position is due to a difference in length for an adjacent side. Fortunately, the individual side lengths were measured. Therefore we can determine how the individual sides deviated from the pyramid mean lengths and how that produced differences in polar orientation.

The data show a direct relationship between improved polar orientation for each structure and improved control of the side deviations. The closer the structures were oriented to the true north pole position the less scatter they had in their side differences from the mean lengths. The engineers not only were continually improving on orientation according to some grand design — they also were continually improving on base construction to maintain individual side lengths to that same grand design.

The data demand that we evaluate the latter. Table II shows the calculated values of base length differences in parts/10,000 from the mean length for the respective pyramids. In this form the data help quantify the continual increase in base length control from Meydum until Menkaure, when a relapse again occurs. See Figure Two. Although the normalized plot tends to accent improved control for larger structures a plot of the real errors shows a similar trend. The normalized plot is useful to show the level of control. Meydum was held to +/- 2 parts /1,000 maximum difference (30 centimeters) among its sides; the Bent enclosure wall was held somewhat tighter. Giza II was held to less than +/- 4 parts /10,000 (8 centimeters) while the Giza I outer casing was held tighter than + /- 1.5 parts /10,000 (3 centimeters). This is remarkable control for such large structures, hardly equaled in modern constructions. As Petrie noted for Giza I, one could cover the error with one's thumb for a length of some 230 meters (1).

(Absolute values means ones ignores the arithmetic sign of the difference.)

and

### Compass Orientations in Minutes of Arc

(The Mean Lengths are in meters.)

 Pyramid Mean N E S W Arithmetic Average of Deviations (Absolute Values) MEYDUM Length 144.32 -8.30 +21.00 -1.40 -12.00 10.70 Orientation -24.41 -35.40 -23.60 -20.60 -18.10 BENT WALL Length 298.70 -3.70 -5.40 -2.00 +11.00 5.50 Orientation -12.45 -4.60 -16.70 (?) -16.10 Giza II Length 215.263 -3.50 +0.37 +2.40 +0.70 1.70 Orientation -5.44 -5.50 -6.20 -5.70 -4.40 Giza I CORE Length 228.638 +0.92 -2.30 +0.26 +1.10 1.20 Orientation -5.26 -4.60 -5.40 -5.40 -5.70 Giza I CASE (P) Length 230.348 +0.65 -1.20 +0.78 -0.22 0.72 Orientation -3.72 -3.30 -4.00 -3.70 -3.90 Giza I CASE (C) Length 230.351 -4.30 -0.43 +4.50 +0.26 2.40 Orientation -3.11 -2.50 -5.50 -2.00 -2.50

The dashed lines on Figure Two are intuitive estimates of the limits of builder control. Future measurement on the two Dahshur structures should show the Bent held to +/- 8 parts/10,000 on side lengths with the Flat held to +/- 5 parts/10,000. Giza II again appears to fit in the sequence before Giza I, rather than after.

Again the Step and Menkaure Pyramids could serve as terminus a quo and terminus ad quem, respectively.

Note that Giza II and the Giza I Core can now be distinguished for difference in control, which did not show in the compass orientations. This fact is important to our data analysis.

We also observe scatter in Cole's data that did not show so prominently on Figure One. See further discussion in companion papers.