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THE SECRET OF THE PYRAMID 55<br />
and the half base to be 1.267843. In such case, the height is<br />
equal to 278.925 cubits and the apothem to 355.245. The volume<br />
now is exactly 18 million cubic cubits, but conditions one and<br />
two are not satisfied. As one can see from these examples, the<br />
three conditions are incompatible with modern mathematics<br />
using the decimal system. But the Egyptians did not use such a<br />
system; instead of decimal parts they used fractions. And if we<br />
use fractions, these problems disappear.<br />
For the Egyptians, as for all<br />
ancient mathematicians, the factor<br />
V was 22 divided by 7, or the fraction—22/7 in decimal expression<br />
3.14857. The factor (j> was the fraction 196/121, or<br />
1.619834. If expressed as simple fractions both factors are related<br />
because the square root of factor cf><br />
is now equal to 4 divided by<br />
factor TT, or 1.272727. Here you have the secret of the Great Pyramid,<br />
or at least one of its secrets.<br />
With this factor, 1.272727, and a half base of 220, the height is<br />
exactly 280 cubits and the apothem 356.089. The volume is<br />
18,069,333 cubic cubits. The first two conditions are fulfilled in<br />
Egyptian fractions but the third is not. To satisfy it we will have<br />
to discover another secret of the Great Pyramid—that its<br />
contrary to previous assumptions, is not exactly a square.<br />
One of the strange qualities of the Great Pyramid is<br />
base,<br />
the fact<br />
that its faces are not entirely flat. They are concave and the<br />
apothem recedes by about one cubit. The first to discover this<br />
concavity was Edme Frangois Jomard, one of the French scientists<br />
accompanying Napoleon on his Egyptian expedition in 1798.<br />
A sketch of the Great Pyramid done by Napoleon himself is still<br />
extant and it clearly shows the receding apothem on the two visible<br />
faces. This anomaly was forgotten for nearly a century until,<br />
in 1881, Sir Flinders Petrie rediscovered it and measured it to be<br />
37 inches, or 1.8 cubits, on the north face. This value was too<br />
big, but what can you expect from ancient measurements? Besides,<br />
there is now an excellent modern aerial photograph showing<br />
the dihedral angle of the sides in superb clarity.<br />
As could be expected, each pyramidologist has his own explanation<br />
for this angle. Fact is that it renders the outlines more distinct<br />
and the shadows more recognizable, which was of great importance<br />
for the astronomers because it made their observations<br />
much more precise. Also the luminosity of the faces is enhanced
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