There should no illusions about the material in this analysis. It is drawn from absolutes in number and geometry, from the intrinsic qualities of observed and observable phenomena at Giza, and from the works of Plato. The matching of data, deductions and absolutes is either perfect or so consistently good as to be beyond the realm of coincidence.
Plato's reputation hardly needs enhancement but, as demonstrated, not only was he brilliant at philosophy, he was a genius with numbers too. It is fitting to conclude with one of his most imaginative mathematical conceptions and a memorable recapitulation of what is encrypted in the Great Pyramid's primal design seen, in this instance, from a slightly modified perspective.
The Atlantis race track
The inner citadel of Atlantis is surrounded by rings of land and water as mentioned in point (i). The largest ring island is three stades wide - see the illustration in point (i). Its outer edge is 10.5 stades from the centre of the circular arrangement, the inner edge 7.5 stades (Lee, pp. 139 and 152). Plato says of this ring island3):
"On the middle of the larger island in particular there was a special course for horse-racing; its width was a stade and its length that of a complete circuit of the island which was reserved for it. Round it on both sides were barracks for the main body of the king's bodyguard." (Lee, pp. 140 - 1)
The island is thus divided into three bands each one stade wide. The outer edge of the race track is 9.5 stades from the centre of the arrangement, its inner edge 8.5 stades. Taking pi to be 22/7 in the calculation, the area of the race track works out to be 56 4/7 square stades. The interest now is in terms of square mile.
The stade, as shown, is 7291 2/3 inches. For ease, the conversion of the stade area to its square mile equivalent is shown in two steps:
(It is easier to do this on a calculator that has memory facilities.)
Step 1. Convert to square inches by multiplying 56 4/7 square stades by 7291 2/3 inches twice;
Step 2. Convert the outcome to its square mile equivalent by dividing by 63,360 (inches in a mile) twice.
The area is 24,609,375/32,845,824 (0.749239081 ... ) square mile.
Divide the measure of the world 24,857 21/22 miles by 24,609,375/32,845,824 and the quotient is 33,177.6.
The number 33,177.6 can be expressed as 24 × 24 × 24 × 2.4. The two other bands produce equally remarkable results. The most outstanding material of all on Atlantis, though, is presented in NADIAE.
The Great Pyramid, a great mnemonic
In the Preamble and point (a) the nature of ancient Egyptian measure and the characteristics of the Great Pyramid were discussed. In point (b) a primal Great Pyramid with a full base of two units, a height of 14/11 units, and a volume of 56/33 cubic units was examined. In this final view of the structure the full base measure is taken as one unit, the height, proportionally, as 7/11 units. Accordingly, the volume becomes 7/33 cubic units.
The fraction 7/33 can be added to a distinctive family of seven and eleven-based fractions that includes 22/7 and 99/70. It has a very large relative: an ancient Egyptian degree is equal to 7,000,000/33 royal cubits (69 3160/63,360 miles).
Furthermore, the quotient of the number of miles in the ancient Egyptian measure of the world 24,857 21/22 divided by 7/33 is 117,187.5. This number, too, has a relative: the product of 17.6 (the number of inches in a common cubit) multiplied by 1.171875 is 20.625, the number of inches in a royal cubit. As well, the time number 24 dimidiates to another but smaller relative, 0.01171875. One can now sense or begin to apprehend the nature of the remarkable underlying geometric matrix, part of which has already been presented, that connects and illuminates everything set out in this paper.