Journal of Geomancy vol. 3 no. 1, October 1978

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CHEPHREN’S PYRAMID
AND THE SEARCH FOR ANCIENT ASTRONAUTS

by Robert Forrest

The publication of M.W. Saunders’s booklets (1) relating the structure of the Great Pyramid to numerical facts concerning Mars and its satellites has prompted me to investigate just how easy it is to ‘relate’ a pyramid to various numerical facts concerning the planets and their satellites. 

I decided to use Chephren’s Pyramid, the second pyramid at Giza, the salient measurements being as follows (refer also to Fig. 1):

Geometry of Chephren's pyramid
Mean base side (b)=8474.9″PETRIE (2)
Angle of slope of faces (B)=53° 10′ ± 4′
Height (h)=5664″ ± 13″
Passage axis displacement, east of middle of north face (f)=490·3″
Chamber east of centre (e)=47″
Upper passage angle=25° 55′EDWARDS (3) angles to horizontal
Lower passage angle=21° 40′

From these figures, the following are easily derived:

Semi diagonal (d)=5992.7″
Diagonal (2d)=11985″
Sum of diagonals (4d)=23971″
Face edge (a)=8245·8″

Let us begin with angle B.  Petrie believed that it indicated that Chephren’s pyramid was constructed from a 3:4:5 Pythagorean triangle (4) and that tan B = 4/3 was the intended angle (this would make B = 53° 8′).  We shall adopt the theoretical slope. 

It is a fact that:

4=Siderial Period of Hyperion (accuracy 0.08%)
3Siderial Period of Titan

this being the first of many links with Saturn and its satellites.  Here are two others:

sin A= h=Siderial Period of Mimas =Siderial Period of Tethys
aSiderial Period of EnceladusSiderial Period of Dione

with respective accuracies of 0·1 and 0·4%. 

Two rather more general results are:

cos A= d=Mean Venus--Sun distance (accuracy 0.5%)
aMean Earth--Sun distance
cos C= ½b=Orbital Period of Uranus (accuracy 0.8%)
aOrbital Period of Neptune

(N.B.  Orbital period in sense of Siderial Period) {8}

And again, the face gradient of 4/3 can be related to the satellites of Uranus, thus:

4=Mean Orbital Period of Oberon (accuracy 0.3%)
3Mean Orbital Period of Titania

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It was C.P. Smyth who first pointed out that the height of the Great Pyramid multiplied by exp(9) (see note 5) gave the mean Earth–Sun distance.  M.W. Saunders added that the base of the Great Pyramid multiplied by exp(9) was approximately also the mean Mars–Sun distance. 

Here are some similar coincidences for Chephren’s Pyramid:

h×exp(10)=mean Saturn—Sun distance (accuracy 0.8%)
2h×exp(10)=mean Uranus—Sun distance (acc. 0.3%)
½b×exp(9)=mean Venus—Sun distance (acc. 0.5%)
d×exp(6)=Equatorial circumference of Neptune (acc. 0.1%)
2a×exp(6)=mean radius of Io’s orbit about Jupiter (0.7%)
2a×exp(7)=mean radius of Ganymede’s orbit about Jupiter (0.5%)
4d×exp(4)=Equatorial radius of Venus (0.6%)
4d×4000=Equatorial radius of Mercury (0.2%)
4d×40 000=Equatorial radius of Neptune (0.6%)

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Ground plan of Chephren's pyramid

Referring now to Fig. 2, we move to consider the displacements of passages and chambers. 

e/f=Polar flattening of Saturn (1.4%)
f/b=Orbital eccentricity of Saturn (4%)
 =Polar flattening of Jupiter (2.5%)
e/b×10 =Mass of Mercury(0.8%)
Mass of Earth
p/q=3√2 (0.1%) (see note 6)

Now to the passage angles.  These can be accounted for as follows:

 Inclination of Ecliptic to Celestial Equator=23°27′
less:Inclination of Mars Orbit to Ecliptic=51′
   21°36′
Lower Passage Angle=21°40′
error= 4′
 Inclination of Ecliptic to Celestial Equator=23°27′
plus:Inclination of Saturn’s Orbit to Ecliptic=29′
   25°56′
Upper Passage Angle=25°55′
error= 1′

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Finally, and following an idea of M.W. Saunders, we use Chephren’s Pyramid to indicate an orbit in the Earth’s Equatorial Plane by sighting along a line joining the mid-point of the north face base to the vertex (fig.3 below)

Possible satellite orbit determined by Chephren's pyramid

The distance OQ, taking into account the oblateness of the Earth, works out to be 31  778 km, a distance which equals 5 times the Equitorial|Equatorial radius of the Earth (acc. 0.4%).  Also, a satellite orbit having this radius, and orbiting in the same direction as the Earth rotates, would have an apex transit period of 1·852 days.  That is, the interval between consecutive appearances of a satellite at the apex of a pyramid, as viewed along the line PQ, would be 1·852 days, which is very nearly 1/16 part of the period between consecutive New Moons (accuracy 0.3%).  Further, {9}

 Apex Transit Period1·852days
lessEarth’s Rotation Period1.000days
=0.852days = 2 × Siderial Period of Axial Rotation of Saturn (0.1%)

If our hypothetical satellite were to orbit in the opposite direction to that of the Earth’s rotation, its apex transit period would be 0·3937 days, which happens to be, curiously enough, the number of inches to a centimetre.  A hundred apex transit periods would therefore amount to 39.37 days which equals 4/3 × the period between consecutive new moons (0.01%).  And that brings us more or less back to where we started, since 4/3 is the tangent of the face slope angle B …

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Either these coincidences reveal a planetary basis for the design of Chephren’s Pyramid, or else they show that it is relatively easy to invest the dimensions and proportions of any pyramid with unintended planetary associations.  I believe the latter explanation to be the true one – both for M.W. Saunders’s Martian theory of the Great Pyramid, and for the coincidences of the present article.  Anyone with an electronic calculator and a little patience might like to ‘have a go’ at the Pyramid of Mycerinus, the third pyramid of Giza. 

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NOTES.

(1) Destiny Mars (1975); Pyramid–Mars Connection (1976); Extra-terrestrial Databank on Phobos (1976).  All from Downs Books, Caterham, Surrey.  Reviewed in JOG 1/4

(2) Pyramids and Temples of Gizeh (1883)

(3) Pyramids of Egypt (1947)

(4) R.J. Gillings, in his Mathematics in the Time of the Pharoahs (1972), appendix 5, remarks that the Egyptians probably did not know the Pythagorean triangle, nor any particular case of it, including the 3:4:5.

(5) For convenience, ‘exp(9)’, is taken to mean ‘ten to the power of nine’, etc. 

(6) The Great Pyramid has been claimed to ‘square the circle’, so why shouldn’t Chephren’s Pyramid be allowed to duplicate the cube?  According to measurements given in Edwards’s book (note 3), the Pyramid of Sahure has a height to semi-base ratio of 3√2, so here we have another ‘instance’ of the Egyptian ‘duplication of the cube’.  Yet another instance is provided by MacHuisdean, in that most bizarre of pyramid books The Great Law (1924), where the Great Pyramid itself is shown to duplicate the cube to an accuracy of 0.1%. 

N.B.  Astronomical quantities used in this article are from the 1976 B.A.R. handbook.