THE GRANITE CASING
The Third Pyramid had a characteristic that is missing in the other two pyramids of Gizah: the lower part of its casing was not of Tura marble, but of granite brought down the Nile from the area of the First Cataract. I have already mentioned the strong visual contrast between the gleaming white upper part of the pyramid and the reddish lower part. The contrast was so great that Diodorus reports that the lower part was black. The important fact is that the Egyptians assigned great significance to these contrasts of color and light.
Petrie observed that the lower part of the pyramid covered by granite reached a height equal to ¼ of the total height of the pyramid, but he did not articulate what is implied in this observation: The granite covered the lower quarter of the apothem (slant height). This second figure, even though implied in the preceding one, is more significant because the granite actually followed the line of the apothem.
In theory the granite casing divided the pyramid as follows:
51° 08’ 02.6989”
As I have said, the slope was practically calculated as 51° 08’ which makes the height of the pyramid 124.5753136 cubits = 65,402.040 mm. In turn this height may have been computed as being roughly 94 4/7 cubits = 65,400.0 mm., divided into a section of 31 1/7 cubits = 16,350 mm., covered with granite, and a section of 93 3/7 cubits = 49,050 mm., covered with Tura limestone.
The most meaningful datum is that the granite casing covered 7/16 of the entire surface of the pyramid. The figure of the surface covered by granite is much more important than the point of the vertical height reached by this casing. This issue apparently did not occur to Petrie. But this is an important mathematical datum that must be related to the fact that in the Third Pyramid surface is what matters.
Herodotos says that the Third Pyramid is covered by ”Ethiopian Stone,” to ”about the middle.” The text reads eis to hemisu, which in Greek means ”to the half” or ”to about the half”; he means that almost half of the surface was of granite.
Since the surface of each face was 16,064 square cubits, the part covered by granite, being 7/16, was 7 X 1,004=7,028 square cubits. In the entire pyramid 28,112 square cubits were covered with granite. The meaning of this figure is best conveyed by statements of Herodotus to the effect that about half of the outer surface of the pyramid is covered by ”Ethiopian stone,” a stone that could be found only at the southern boundary of Egypt and beyond it.
The entire pyramid was calculated by the number 64 (= 8 x 8 or 4 x 16); hence, it is not surprising that the amount covered by granite was set at 7/16 of the total surface (that is, 43.75 percent). The important question is whether the difference in surface between the area covered by granite and the area covered by Tura marble was intended to correspond to the difference between the part of the Northern Hemisphere covered by land and the part covered by water. In current textbooks of geography one often finds the statement that the relation between land and water is 4:6. The most precise figure I could find in the texts is 39:61. Modern geographers are satisfied with the ratio 4:6, because it is very difficult to be more accurate.
Areas occupied by estuaries, by coastal waters and by small islands produce uncertainty in calculation. Today we can use computers and mechanical scanners; however, these have to be applied to detailed maps, but maps provide different figures for surface according to the type of projections used in the map. Because any map involves the reduction of a curved surface to a flat surface, any map involves a distortion of the data. There are special types of projections in which one tries to preserve the identity of proportions between areas on the map and areas on the surface of the earth. This can be achieved by sacrificing other elements, such as equal scale in the distances between localities. But, there is no type of projection that can provide a perfect solution. Any projection system adopts some sort of compromise.
If the Egyptians really meant to indicate that about 7/10 of the Northern Hemisphere is covered by land, it follows that they had astoundingly precise information about the coasts of the continents in the Northern Hemisphere.
Unfortunately in this case we cannot arrive at the absolutely perfect numerical fit that would give a certain answer to the question.
We have to keep in mind two sets of facts. One, the Third Pyramid was erected in order to represent the surface of the Northern Hemisphere. This pyramid is the only one of the three pyramids in which the surface is built of two different kinds of material. The part covered by granite is 7/16 of the entire pyramid; the use of this material greatly increased the cost of construction, but was in part compensated by making the Third Pyramid small The Third Pyramid is half the scale of the Second Pyramid.
Two, the Northern Hemisphere differs sharply from the Southern Hemisphere, in that, whereas the latter is covered mostly by oceans, the surface of the former is in great part land: almost half of it. If the Third Pyramid was intended to indicate that the Northern Hemisphere is covered by land in proportions of 7/16 of the total surface, the Egyptians come as close as practically possible to the correct figure. The Egyptian figure means 43.75 percent. The Encyclopedia Britannica quotes the available calculation that tries to be as precise as possible, 39 percent.