The Keys of Atlantis

A Study of Ancient Unified Numerical and Metrological Systems

by Peter Wakefield Sault

Copyright © Peter Wakefield Sault 1973-2008
All rights reserved worldwide

3-2. Earth and Moon

The Earth has an irregular shape, called the geoid. Its closest regular relative is the oblate spheroid (or flying saucer), which can be closely approximated by a Reference Ellipsoid, as already employed previously in Chapter 2. We shall continue to use that model here but will add to it a further abstraction, the Reference Sphere, whose size we shall here determine on the basis of what may seem at first sight to the reader to be a strange set of operations.

Ignoring topographical details, the Moon is an almost perfect sphere whose mean radius is expressed by astronomers in terms of the Earth's equatorial radius, as a coefficient, k, equal to 0.2725076. From this it may be calculated that the mean radius of the Moon is 1,738,090.5m.

For our purposes we are going to calculate a range of analogs to k for all latitudes, working back from the mean radius of the Moon. The figure quoted above represents only one end of that range. The other end is calculated by finding k in terms of the Earth's polar radius. This gives us a figure of 0.2734243 for the upper boundary of the range.

Having obtained the limits of the range we can identify the simplest whole number ratio that falls within it. A few simple calculations reveals that ratio to be 3:11, which evaluates to a k of 0.272727...

We can now obtain the radius of the Earth corresponding to this value by dividing it into the Moon's mean radius. This gives us a figure of 6,372,998.5m. This we shall designate our Reference Radius. We can further proceed geometrically to diagram the proportions of the two bodies by treating the Earth as though it were a sphere of that radius, the Reference Sphere already mentioned.

Figure 3-A. Graph of Radius vs Vertex Latitude

With the calculated diameter of the Earth across the 29.294° parallels the ratio of the diameters of Earth and Moon may be reduced to one of small whole numbers; 11:3 to be exact. Taking this as a cosmic metrological base gives a unit of length equal to one third of the diameter of the Moon and to one eleventh of the diameter of the Earth across the 29.294° parallels. Thus the two diameters add up to 14 such units. Drawing two touching circles in the same proportion, 11:3, as shown in Figure 3-1 below, representing Earth and Moon, a third circle may be struck from the centre of the Earth through the centre of the Moon. In terms of the units derived from the ratio of the diameters, the radius of the third circle is 7 and, taking p (pi) as 3¹/₇, its circumference is 2 × 22/7 × 7 (i.e. 2pr), or 44. Now, since the diameter of the Earth is 11, the length of the perimeter of a square drawn around the Earth will be four times that, or 44. Thus the circumference of a circle whose radius is equal to the sum of the radii of Earth and Moon is the same length as the perimeter of a square around the Earth.

Figure 3-B. Earth and Moon Juxtaposed

It must be said that the preceding statement assumes several essentially false premises. The first of these is the value of p as a ratio of two whole numbers, 7:22. This particular approximation exceeds the true value by 0.04%. The true value of p, however, cannot be expressed. Were we to use the true value then we would not be looking at a ratio of 14:11 (combination circle to Earthdisk respectively) in the figure of the Earth and Moon, but at ¼p or approximately 0.785398..., which again cannot be expressed as a ratio of whole numbers. The second is treating the Earth as a sphere whose diameter relates

This model is based in the first place upon finding that particular diameter of the Earth which relates to the diameter of the Moon by the simplest possible ratio of whole numbers and by then assuming the Earth to be a sphere of that diameter so that it may have a square drawn around it all four sides of which touch it. In this figure we discover the well-known approximation to p (pi).

1.		Peter Tompkins, Secrets of The Great Pyramid, 1971, p.xiii
2.		ibid. p.217
3.		ibid. pp.30-31
4.		ibid. p.77 (footnote)
5.		Livio Catullo Stecchini, Notes On The Relation Of Ancient Measures To The Great Pyramid, included as an appendix to Secrets of The Great Pyramid, 1971, p.323
6.		Herodotus, The Histories, circa 440 B.C.
7.		W.M.F.Petrie, Seventy Years in Archaeology
8.		W.M.F.Petrie, The Pyramids and Temples of Gizeh, 1883, P.88
9.		ibid. p.27
10.		ibid. p.28