Around CarnacAn extensive megalithic complex in southern Brittany, western France, predating the British megalithic. in Brittany the land is peppered with uniquely-formed megalithic designs. In contrast, Great Britain’s surviving monuments are largely standing stones and stone circles. One might explain this as early experimentation at Carnac followed by a well-organised set of methods and means in Britain. What these experiments near Carnac were concerned with is contentious, there being no appetite, in many parts of society, for a prehistory of high-achieving geometers and exact scientists. Part of the problem is that pioneers interpreting monuments are themselves hampered by their own preferences. Once Alexander ThomScottish engineer 1894-1985. Discovered, through surveying, that Britain's megalithic circles expressed astronomy using exact measures, geometrical forms and, where possible, whole numbers. had found the megalithic yardAny unit of length 2.7-2.73 feet long, after Alexander Thom discovered 2.72 ft and 2.722 ft as units within the geometry within the megalithic monuments of Britain and Brittany. as a likely building unit, he tended to use that measure to the exclusion of other known metrological systems (see A.E. Berriman’s Historical MetrologyThe application of units of length to problems of measurement, design, comparison or calculation.. Similarly, John Neal’s breakthrough in All Done With Mirrors, having found the foot we still use to be the cornerstone of ancient metrology, led to his ambivalent relationship to the megalithic yard. Neal’s interpretation of the Crucuno rectangle employs a highly variable set of megalithic yards, perhaps missing the simpler point, that his foot-based metrology is supported as present within the dimensions of the Crucuno rectangle; said by Thom to be a “symbolic observatory” of the sun: this monument was an educational device, in which Neal finds the geometry of “squaring the circle” which, as we see later, was probably the Rectangle’s main metrological meaning.
Figure 1 Alexander Thom’s survey of Crucuno Rectangle by Alexander Thom, see MRBB, 1978, 19 & 175-176
Since the sun rose and set (at the two solsticial extremes of Winter and Summer) away from east-west by the lesser angle of a 3-4-5The side lengths of the “first” Pythagorean triangle, special because the side lengths are successive small primes and, at Carnac, defined the solsticial extremes of the sun. triangle the builders of Crucuno created a rectangle of standing stones whose longest sides ran exactly east-west. It was made four units long relative to three units north-south. The resulting diagonals between opposite corners were then automatically aligned to the solstitial extremes of the sun. Thom made an accurate survey of the monument which he identified as 40 by 30 megalithic yards or thereabouts, depending on how one deals with the thickness of the stones in a relatively small monument. Thom’s survey of Crucuno has recently by validated using a 3D scan .
Figure 2 Orientation and 4:3 side ratio of Crucuno defining solsticial sunrises and sets in winter and summer
Figure 3 Midsummer sunrise 2007, between stone 6 and 7, when above the trees. (The alignment is less accurate today)
If one takes
Thom’s figure for the megalithic yard of 2.72 feet, 40 such yards
equal 108.8 feet.
Rounding the figure
108 feet makes it little
different and, given past assumptions, 108 feet equally fits as in inscribed
rectangle within the stones. This number of feet has many unique properties. For example, 100 feet of the Drusian
variety (27/25 [1.08]
feet) equal 108 feet,
making a megalithic yard/step of 2.7 feet, which is then the root module of the
Astronomical Megalithic Yard or AMYA megalithic yard which, in inches, expresses the true astronomical ratio of mean solar months to lunar months.. An explicit AMY is found within 4Km east of Crucuno, marked in the end stone (C3) of Gavrinis (see figure 4), alongside the foot
and the royal cubit3/2 feet of any sort, such as 12/7 {1.714285}, 1.5 Royal feet of 8/7 feet, but sometimes a double foot, such as the Assyrian {9/10} of 1.8 feet. of 12/7 feet.
The foot, royal
cubit and AMY were all astronomically derived
since the chambered cairn of Gavrinis is oriented to the solar
and lunar extremes
of the south east quadrant.
Figure 4 The left-hand end stone called C3 within which day-inches, the foot, the royal cubit and AMY are all shown, within astronomical and monumental contexts [figure 5.10 in Sacred Number and the Lords of Time. 131.]
The length 108 feet can be viewed in many ways and we can try a few. It is 63 (9 x 7) royal cubits and that length, having a factor of seven, could be a convenient diameter when multiplied by the pior π: The constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159, in ancient times approximated by rational approximations such as 22/7. of 22/7The simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods.; the seven divides to leave a circumference of 22 x 9 (198) royal cubits. The shorter side of the Rectangle in these units is then 3 x 63/4 = 47.25 royal cubits whilst one quarter of the Circumference is 198/4 or 49.5 rotal cubits, the side length of a square of equal perimeter length. The four-by- three geometry cannot therefore square the circle with its shorter side length, being deficient by 2.25 royal cubits (3 and 6/7th feet), though it is close to doing so, and therefore compatible within the monument. When John Neal extended the 4 x 3 rectangle to the south he found the required the side length for the southern kerb to achieve the squaring of the circular perimeter (63 royal cubits in diameter in figure 5). This adjustment allowed five otherwise spare stones of the southern kerb, numbered 13-17 in Thom’s survey, to be part of that extended geometry.
Figure 5 Neal’s extention of the Rectangle to find five otherwise “spare” stones of the southern kerb apparently defining the “squaring of the circle” as a new shorter side of the rectangle
Figure 5 clearly shows that the southern kerb was extended southwards, from being a 4 by 3 rectangle, so as to include the similarly-sized rectangle required for the squaring of the circle, with a 4 x 3 rectangle having astronomical virtues. The stones numbered 3, 5, 8, 12, 16, and 20 could each have been part of this plan, touching as they do the circle’s perimeter at significant points of crossing. Stone 8 appears to have a contour to follow the circle and a twin stone 20 opposite it [see also Neal. All Done With Mirrors, pp164-5].
If these two interpretations are correct, the Rectangle demonstrated the geometrical peculiarity of the solsticial sun at Carnac in 4000 BC, in rising and setting across the diagonals of Crucuno’s 4 by 3 rectangle; whilst also demonstrating the squaring of the circle. Neal’s metrology for Crucuno used megalithic yards varied by one part in 175 and in 440, and this may not reflect how the builders of the Rectangle chose their measures to design it.
For example, the east-west length might have been chosen (for numerical reasons) to be 108 feet, being 4 times 27 feet. When divided by the royal foot of 8/7 feet, (108 x 7/8) x 22/7 causes seven to cancel, as too the four in 108 leaving 27 x 11 = 297 royal feet as the circumference and the equal perimeter square. The square is an important structure since its dimensions are linear rather than radial, enabling easy definition of ropes whose length is 297 royal feet, which equals 125 Astronomical megalithic yards (AMY) of 2.71542857 feet. We can see that the AMY as 176/175Ratio crucial to maintaining integers (see geometry lesson 2) between radii and circumference of a circle, and crucial to the micro-variation of foot modules in ancient metrology. of the Drusian step of 2.7 feet, is the key to a geometry involving implicit cancellations causing the Drusian module transformed into its root canonical form and the AMY. This was the AMY John Neal recognised on Lundy Island, in 2001, as being the 176/175 variation of the root Drusian module, Robin HeathEngineer, teacher and author, who discovered the Lunation Triangle (c. 1990), that enabled the lunar year to be rationally related to the solar year. During the 1990s we collaborated to further understand the astronomical and numerical discoveries of the megalithic astronomers. having established its length some years before from both measuring British monuments and calculating the astronomical excess of the solar yearFrom Earth: the time in which the sun moves once around the Zodiac, now known to be caused by the orbital period of the Earth around the Sun. over the lunar year, when these years are counted using megalithic yards as lunar months.
Figure 6 The key metrological transformation at Crucuno
The 40 Drusian steps of the 108 foot Rectangle leads to a circle whose circumference is 125 AMY, the AMY being 176/175 longer than the Drusian step of 2.7 feet. The formula for 176/175 is 4/25 x 44/7, the cross-multiplication of two different approximations to Pi. We actually use the more accurate 22/7 as pi whilst the 125/40 of circumference to diameter has produced a pi of 3.125, as the effective pi preserving integer units that differ by 176/175. This is a general property of the ratio of 176/175 which is why it was so useful in the megalithic when dealing with circular geometries governed by pi.
However, the lunar month (29.53) divided by the lunar orbit (27.32166) is, at 1.08085, closely 27/25, the Drusian foot and this makes this particular example primary for demonstrating the close affinity of the lunar orbit, month and years and the solar year.
The squaring of the circle naturally allows integer units to describe the diameter, circumference and equivalent square perimeter when one uses the same unit enlarged by 176/175 to measure these perimeters. The circle is actually theoretical whilst the square perimeter is practical since it can be both deduced from the diameter and measured for the formation of longer lengths. 125 AMY is half of a Drusian stade of 625 such feet and one 16th of a Drusian mile of 5000 of those feet. (n.b. The stade was the unit of field measure found by archaic Greece and the mile is traditionally eight stades equalling 5,000 feet, the English stade being the furlong of 660 ft x 8 = 5280, based then of 600 Saxon feet of 11/10 ft)
Conclusions
It is perhaps no coincidence that John Michell created a numerical cosmology on the squaring of the circle whilst his collaborator in recovering ancient metrology from its historical debris was John Neal, who finds that geometry at Crucuno. As I proposed in Sacred Number and the Lords of Time, metrology is more probably innovated by the megalithic than by an unknown “civilisation X” like Atlantis, unless that myth is about the megalithic – about whom there are concrete facts due to their monumentalism. What Thom called a “symbolic observatory”, what Michell anticipated in his New Jerusalem geometry, which Neal found expressed at Crucuno, using the ancient metrology restored by Neal and Michell, we find here to be also a lesson in astronomy and metrology and a general-purpose geometry for manufacturing units of length which are 176/175 greater than the units used to define in its diameter. In particular, astronomical megalithic yards could be manufactured from a length of 40 Drusian steps (108 feet). Since the 4 x 3 geometry for solsticeThe extreme points of sunrise and sunset in the year. In midwinter the sun is to the south of the celestial equator (the reverse in the southern hemisphere) and in midsummer the sun is north of that equator, which is above the geographical Equator). sun events on the horizon was very similar to that required for squaring the circle: The three of 4 x 3 becomes 3.142857 or pi as 22/7. The ratio of 4 to 22/7 is the ratio of a square to its in-circle.
Figure 7 The squaring of the circle, prefigured in the 1/4 circumference of a circle and the side length of its out-circle. This ratio of 22/7 (3.142) to a side length of 4 is the ratio of Crucuno’s smaller side length to its longer dimension, clearly four units in order to make the 3-4-5 triangles as the diagonals aligned to solstice events. Far from theoretical, the Crucuno rectangle, in its full height, could manufacture 125 AMY from a length of 40 Drusian steps.