The geometry is clearly affected and complicated by the often-quoted fact that the various rings have slightly different centres. Yet we have seen that the construction
phases of Stonehenge are attributed to up three distinct sets of "builders" and over a span of up to 1500 years. Considering however that the circle centres may vary by up to two feet the model is a good
predictor of the R holes, the Sarsen Circle, the Z and Y holes, the
Aubrey Circle, stone hole C, stone hole B, and the Heel Stone. It is less compelling as a model if we consider both the Inner
Ditch diameter and Counter Scarp. This of course fits neatly with the analysis of Cleal, Walker and Montague, who believe that the earthwork axis was some considerable distance away from the axis of "phase 3" from which
the ring series is drawn. Interestingly, and I think probably significantly, the Avenue ditch diameter mirrors the Sarsen Circle diameter and it is in the north and north east sections that the ditch diameters best
fit the model. Working to such a rigid plan over the constructional timeframe would inevitably produce errors, which coupled with our lack of understanding of how accurately the builders interpreted the plan, probably
accounts for its variations. For example, most authorities agree that the "Z" and "Y" holes give every indication of being purposely
arranged in a spiral, but it is entirely possible that these holes, which are attributed to the last stages of building, were an adaptation of the earlier design and marked a cultic shift from circular to spiral
geometry. Alternatively and perhaps more probably, the seemingly haphazard arrangement of the "Z" and "Y" holes is entirely due to our
incomplete understanding of the build sequence and the unwarranted assumption that all the holes were built at the same time, which as we have seen is contradicted by the archaeology. Such a design would have
posed considerable surveying problems for megalithic man on flat terrain and as we know Stonehenge is sited on a slope. So why they should go to this considerable trouble is indeed puzzling and is not entirely answered
by astronomical considerations. Yet it has been demonstrated that astronomy probably played a vital role in the development of Stonehenge, which leaves us with the unanswered question of whether the two practices
were independent of one another. It is I think pertinent that in the period when the Trilithons were erected the builders went to considerable trouble attempting to level the tops of the stones. This is the mark
of symbolism, having no bearing on astronomy and is further evidence that in its later stages Stonehenge had evolved into a purely ritualistic monument. However there is nothing in the geometry that necessarily
indicates a detailed understanding of the square root of three, as all of the rings can be easily drawn by classic Euclidean techniques. Although there is suspicion that it is unlikely this detailed mathematical design
was constructed geometrically without a corresponding understanding of the square root of three. But viewed in isolation, the striking fit of the Stonehenge Ring system to a mathematical model based upon
root three, lacks comparative support. There are however other megalithic monuments in the area which shed light upon the whole thesis of root number constructional technique. The first of these is the neolithic monument of Woodhenge. Only a short distance away from Stonehenge lies the Neolithic monument of Woodhenge, so named because of
its similarity to Stonehenge and because it was constructed with wood rather than stone. Now Woodhenge was arranged with both mathematics and astronomy in mind. Astronomical, because the elongated axis points to
midsummer sunrise; and mathematical because the ring diameters are multiples of the first radius. Although oval in shape the "long" diameters of the six post rings that make up the monument are (in metres) as
follows:- F E
D C
B A
11.7 17.6 23.4 29.3 38.1 43.9
Maud Cunnington who excavated the site believed the groundplan for the rings had been scribed circles, which were then squashed into ellipses. As to the reason for this she had no explanation. Now, if we take
the diameter of the first post F
and divide it by two to obtain a radius we get the figure of 5.85. Curiously we find the first four posts are almost exact multiples of this radius. 11.7 plus 5.85 equals 17.55. Then 17.55 plus 5.85 equals 23.4, followed by 23.4 plus 5.85 equalling 29.25. There the mathematical symmetry appears to stop. Yet the first four diameters clearly indicate a mathematical certainty, which demonstrates an ability to construct an exact design. This was no incompetent savage laying the plan out by eye. It was a considered and purposeful design. So if the first four rings were multiples of the radius why did the last two deviate from this rule? Well if we assume that post ring
B was measured wrongly and that its true position should have been 38.03 instead of 38.1 we find that all the post rings are multiples of 5.85 with the ratios being as follows:-
F E
D C
B A
2 3 4 5 6.5 7.5
So the enigma becomes further compounded by the appearance of the last two ratios, which cannot be constructed without some practical ability in geometry or mathematics.
Consequently we can see that the circular rings of Woodhenge were arranged to a simple mathematical and hence a geometric pattern. I have shown that Stonehenge follows an altogether more sophisticated geometry, which
implies at least a putative understanding of square roots and in particular the square root of three. At this stage it would be possible to conclude that the design intent could have been religious or perhaps a
prehistoric attempt to determine Pi, as such calculation in positioning is entirely irrelevant to any astronomical alignments. However the respective geometries of Woodhenge and Stonehenge are markedly different
considering they are supposed to be contemporary. One is a simple mathematical series, the other far more complicated and so there seems to be no real connection between them. However there is another circle worth
commenting upon, which gives every indication of providing the smoking gun of geometric similarity and demonstrates that the sophistication of Stonehenge was not unique. |
