Picture by krautrock, a member of megalithic.co.uk in June 2010.
Figure 1 Alexander Thom’s site plan, with cardinal directions and highlighting the diameter .
It is tempting to assume geometry within stone circles and this one invites that by having eleven regularly placed stones,. However, 11 is rarely found in regular geometries or stone circles.
But,
- Eleven is associated (geometrically) with the simplest approximate ratio for 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. and, being on a circle perimeter 22 units on the perimeter means 7 as the diameter. However, the diameter here is 7 x 9 = 63 so that 7 units of 9 feet in diameter translates into 22 x 9 = 198 feet on the circumference.
- The second symbolism of eleven is found in the solar time cycles of 33This is the number of years for an exact number of 12053 days. This period can be measured using the equinoctal sun and it has come to be known as the lifetime of semi-divine Solar Heroes such as Jesus and Mithras. This period relates geometrically to the 18.618 years of the moon's nodal period. years which traditionally references as the Solar Hero cycle as the age when heroes die. 33 years was signified in this way because of an exact alignment, at which EquinoxThe two times of the year, in Spring and Autumn, when the sun rises directly east and sets directly west - at every latitude on Earth. sunrise should repeat on the distant horizon every 33 years. While 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. is 365 whole days long it takes an extra 32/132 of a day for the Earth’s orbit to complete, and this fraction (of 32/132) depends upon 4 x 33 = 132 losing its 33, 33 years after an earlier Equinox on the horizon. (Note that one did not need to know the data and then calculate, as we do today: instead, observation of in-exact solar risings or settings could notice near exact repetitions occurring after 8 years, but more perfectly after 33 years.
Returning to the circle, the circumference of this stone circle is 198 feet which is 6 x 33 = 198 so that the 11 stones may be referencing 33 solar years.
The 33-year period is strangely linked to the movement of the moon’s nodes, which take 18.618 years (of the nodal periodUsually referring to the backwards motion of the lunar orbit's nodes over 6800 days (18.618 years), leading to eclipse cycles like the Saros.) to progress once around the path of the sun (eclipticThe path of the Sun through the sky along which eclipses of sun and moon can occur, traditionally divided into the 365¼ parts of the solar year, each part then a DAY in angle rather than time.). The area under this precession of the lunar nodes (pi x 18.618^2 = 1,088.970022752789) relative to the earth it orbits, which closely equals the area of a square of side 33 x 33 = 1,089.
The megalithic and ancient world both made monuments conforming to the equal area and 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. geometries and even though the equal area situation is proven unsolvable, one sees that (before the notion of an analytic solution) a perfect example was found of a workable pair of numbers (33 years and 18.618 years) was available as these two very significant astronomical time periods.
If the circle is 63 feet in diameter, then one divided by 14 and multiplied by 11 to obtains the square of equal perimeter: 63 x 11/14 = 49.5, which is 99/2 feet on the side. This can then establish the radius of the circle as 18.618 of the same units: When divided by 33, 99/2 becomes 3/2 which is the unit for the radius of the circle of equal namely 18.618 x 3/2 = 27.927 or nearly 28 feet. Below is a picture showing the square and the circle, equal in area in red while the perimeter of the stone circle is equal in perimeter to the red square.
Author’s notes.
- I have been looking at ways in which 18.618 years could have been generated geometrically so as to avoid the need to resolve it as a numerical measurement, and this has led to some really interesting ideas.
- I came upon Anne Macauley’s book Megalithic Rhythms and Measures (2006) and was interested whether the apparently unique eleven equally-spaced stones were indicative of the Equal Area having been seen as relating the 33-year Solar Hero cycle and 18.618-year Nodal cycle where the latter is a radius and the former is a square’s side-length of 33 years, which the solar year divided into. These numbers have special properties.
- My books on Sacred Geometry: a. Language of the Angels and b. in Ancient Goddess Cultures both have a lot on the equal perimeter model, which describes the relative and absolute sizes of the Earth and the Moon, and the equal area model which fits the 33/18.618- cycles which ratio equal a near-pi ratio of SQRT (3.144).
Phenomenal Visualization
One sees above that the equal area circle touches the recumbent stone and the southern stones tip, and that the maximum moon, in Scotland, can touch the horizon being more extreme to the south than the sun at winter 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)., see below where I have drawn the Moon as a white disc between the two smaller recumbents (off the main one) as if showing the moon between the actual vertical monoliths either side.
One can see that the red circle embraces the recumbent stone
and its altar-like appendages.
This jest of showing “on plan” a vertical structure was seen at Gavrinis L6 where the “sun gate” Manio Quadrilateral feature, 4 Km to the west, is shown in what appears to be a technical information stone originally accompanying the Quadrilateral (as were the other stones lining in the Cairn’s corridor walls.