In 1973, Alexander Thom found the Crucuno rectangle to have been "accurately placed east and west" by its megalithic builders, and "built round a rectangle 30 MY [megalithic yards] by 40 MY" and that "only at the latitude of Crucuno could the diagonals of a 3, 4, 5 rectangle indicate at both solstices the azimuth of the sun rising and setting when it appears to rest on the horizon." In a recent article I found metrology was used between the Crucuno dolmen (within Crucuno) and the rectangle in the east to count 47 lunar months, since this closely approximates 4 eclipse years (of 346.62 days) which is the shortest eclipse prediction period available to early astronomers.
Figure 1 Two key features of Crucuno's Rectangle
About 1.22 miles northwest lie the alignments sometimes called Kerzerho, on the present D781 before the hamlet Kerzerho - after which they were named - on the way north to Erdeven from Plouharnel. These stone rows are the start of a major complex monument but here we consider only the section beside the road to the east. Unlike the Le Menec, Kermario and Kerlestan Alignments, which start north of Carnac, Kerzerho's alignments are, like the Crucuno rectangle accurately placed east and west.
Figure 2 Two stones, angled to the diagonal of a 3-4-5 triangle 235 feet from north west stone and setting sun at summer solstice. The diagonal appears counted in 235 feet as to the Metonic period
235 feet is the number of lunar months in the 19 year Metonic period, so it appears one foot was used to count one lunar month; perhaps using the trigger of the summer solstice sunset as the starting and finishing point for the counting. The sun, moon, and stars should all be in the same alignment after nineteen years, for example there will be the same phase of the moon with the same stars behind it, if visible after sunset.
One can see that 235 lunar months must be divisible by 5, there being 47 lunar months in a fifth of that number. This means that Metonic is in an ideal numerical context as a 5-side count whilst Crucuno, as an eclipse count, was based upon the fact that 47 lunar months are just greater than 4 eclipse years (of 346.62 days,) making 47 lunar months the smallest significant eclipse period, called the Octon because there are eight eclipse semesters (of 173.31 days) in that period. Because of this, the 3-4-5 x 47 lunar months triangle can also be seen as a 12-16-20 eclipse year triangle as in figure 3.
Figure 3 Dualism of time implicit in the Metonic count
Whilst the 19 eclipse year period, called the Saros period, is the definitive eclipse period for predicting near-identical eclipses, the Metonic is a useful eclipse count based upon five Octon periods of 47 lunar months. This count would have naturally allowed the astronomers to find the Saros using the idea of extending Crucuno's 47 month count.
The resulting metrology is very interesting since, dividing 47 lunar months by four very nearly gives the number of lunar months in an eclipse year as 11.75 lunar months. The exact figure is 11.738, less by only 8.5 hours. This means 11.75 feet are the effective units of figure 3's right hand triangle. In fact the stone rows, where coherent, appear to be based upon a row separation of 11.75 feet and so may have formed "avenues" for counting eclipses in a similar way to that proposed for the Crucuno, where eclipse events process with time.
- 11.75 feet is a pole of 10 feet of 1.175 feet long, making the ratio to the English foot 47/40 feet.
As an aside relevant tio later metrology: This foot is indistinguishable in length from the standard canonical Russian foot of 1.176 but in 4000 BCE, the system of ancient metrology was still developing and is thought only becoming codified by the British megalithic after the early phases of Stonehenge, such as the Aubrey circles. The earlier megalithic might be seen as using a Russian foot when in fact they were generating monuments based, as here, on 47 divided by 40.
Figure 4 The 4 by 3 geometry gives rise to a metrological grid
If, instead of the 4x3 rectangle, the 4 x 3.125 (as Pi) rectangle was intended then the extra 0.125 required is equal to half 10.175 ft, allowing the Pi rectangle to be formed with its vertical side the side-length of a square whose perimeter equals the circle formed by the horizontal side as its diameter, figure 5 (see this at Crucuno).
Figure 5 The extended Pi Rectangle for Kerzerho, indicating stones comparable to Crucuno or, on the geometry (both marked in yellow)
The perimeter of the circle and square will be four times the lesser side-length of the rectangle, that is 3.125 x 47 = 146.875 feet. Times 4 this equals 1175/2 (587.5) ft. When this is divided by 22/7 the result is 186.9318, which is 175/176 of the rectangles greater side-length of 188 (4 x 47) feet.
This is the same miracle visible in the Crucuno rectangle, that such a rectangle demonstrates that a unit 176/175 of the diameter or radius will lead to a "canonical" number of units around the circumference of a circle, whilst the Pi rectangle's lesser side is the side of the square of equal perimeter to that circle. There is hence no need to calculate or measure the length of any circle's circumference once this was discovered and used as a microvariation of 176/175 within ancient metrology: the radius or diameter length could, through the Pi rectangle or a varied measure, generate an integer circumference.
In this case, if all four quadrants aligning to the four solstice points was realised (as seems the case prior to agricultural clearance of stones in fields), then the rectangle would double in size then the perimeter of the square would be 1175/2 times 4 or 2350 feet, a number echoing the radius of 235 feet to midsummer solstice sunset. This larger rectangle and the likely methods of counting eclipses will be considered in a later article.