Month: March 2025

Easter Aquhorthies

Easter Aquhorthies (i.e. apocathery) has eleven stones in a circle and in between the two south-to-south-west stones is a large (bridging) recumbent stone, more commonly found in Scottish circles  and associated (by Alexander Thom) to lunar observatories because, in Scotland at lunar maximum standstill, the moon can rest upon or be hidden by a raised horizon.

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,

  1. Eleven is associated (geometrically) with the simplest approximate ratio for pi, of 22/7 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.
  2. The second symbolism of eleven is found in the solar time cycles of 33 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 Equinox sunrise should repeat on the distant horizon every 33 years. While the solar year 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 period) to progress once around the path of the sun (ecliptic). 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 perimeter 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.

  1. 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.
  2. 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.
  3. 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 solstice, 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.