first published in March 2018
In 1973, 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. 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 azimuththe standard angular measurement of angles on the horizon, measured clockwise from zero degrees true North. of the sun rising and setting when it appears to rest on the horizon.” In a recent article I found metrologyThe application of units of length to problems of measurement, design, comparison or calculation. was used between the Crucuno dolmenA chamber made of vertical megaliths upon which a roof or ceiling slab was balanced. (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 alignmentsIn general, to the sun and moon on the horizon, rising in the east or setting in the west.
Also, a name special to Carnac's groups of parallel rows of stones, called Le Menec, Kermario, Kerlescan, and Erdevan. sometimes called
Erdeven, on the present D781 before the hamlet Kerzerho – after which hamlet
they were named by Archaeology. These stone rows are a major complex monument
but here we consider only the section beside the road to the east. Unlike the
Le Manec Kermario and Kerlestan alignments which start north of CarnacAn extensive megalithic complex in southern Brittany, western France, predating the British megalithic.,
Erdevan’s alignments are, like the Crucuno rectangle accurately placed east and
west.
Figure 2 Two stones, angled to the diagonal 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 235 feet from north west stone and setting sun at summer 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).
The Metrology
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 MetonicGreek: The continuous 19 year recurrence of the moon's phase and location amongst the stars. 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 is 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 yearthe time taken (346.62 days) for the sun to again sit on the same lunar node, which is when an eclipse can happen. triangle as in figure 3.
Figure 3 Dualism of time implicit in the Metonic count
Whilst the 19 eclipse year period, called SarosThe dominant eclipse period of 223 lunar months after which a near identical lunar or solar eclipse will occur., 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. 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 footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000]. 47/40 feet.
One needs to remember: 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 became codified in 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 feet.
Figure 4 The 4 by 3 geometry gives rise to a metrological grid
If, instead of the 4×3 rectangle, the 4 x 3.125 (as 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.) 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 Pi Rectangle for Erdeven indicating stones comparable to Crucuno or, on the geometry (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 22/7The simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods. the 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 176/175Ratio 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 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 perimeterA type of geometry where an rectilinear geometry has same perimeter as a circle, usually a square but also a 6 by 5 rectangle whose perimeter is 22, assuming pi is 22/7 or 3 + 1/7. 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 and 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 method of counting will be considered in a later article.