Squaring the Circle in Brittany

Megalithic monuments are sites of learning when one understands the Traditional Arts, especially Astronomy, Geometry, Arithmetic (number) and Metrology. The area around Carnac, Brittany is one of the foremost megalithic complexes and this hence has a lot to teach us.

This year, at the summer solstice, the Plouharnel Tourist Office will be staging a festival focussing on the alignments to the solstice of a number of the megaliths there. The site was probably originally developed there because, at that latitude, the solsticial sun forms a 3,4,5 triangle relative to the equinoctial sun, i.e. the east-west axis. The north-south axis is itself significant because that meridian also runs through Arthur’s Seat in Edinburgh (Rosslyn Chapel) and major Orkney rings such as Brodgar.

The 3,4,5 triangle is the “first” whole number or “Pythagorean” triangle, that is the one with the lowest numbers. As with the Station Stone rectangle at Stonehenge, which is based on the second 12,13,5 triangle, two triangles can form a rectangle three units by four units.

 

Alexander Thom’s site survey for Crucuno, showing the rectangle created by two 3,4,5 triangles

Alexander Thom noted that one of the rectangular stone rings at Carnac, called Crucuno, forms such a rectangle 30 by 40 megalithic yards long. This year, visitors will be encouraged to view the solsticial sun across its diameter since the stone rectangle is aligned east-west, as if to mark the special nature of the latitude of Carnac.

More recently, John Neal has found a second relationship built into this stone ring. The southern extent of the rectangle can show the important relationship in sacred geometry of “squaring the circle”. In this case the height of the rectangle is slightly longer, 31.25 megalithic yards instead of 30, in which a circle with diameter equal to the width of 40 megalithic yards, has the same perimeter as a square of side length 31.25 megalithic yards.

John Neal’s Squaring of the Circle interpretation of Crucuno, after All Done with Mirrors

Neal’s relationship is based on one of the whole number approximations to Pi equal to 25/8 which is 3.125 in decimal rather than around 3.1416. Whilst this may dismay the modern sensibility, there is consistent evidence that approximations to Pi were often used within the ancient science as in the ancient model of the Size of the Earth, where 22/7 and 63/10 are both deployed (see Sacred Number).

 

Raising the Squared Circle to Stone 23 defines the height of the Rectangle of Crucuno

By raising the centre of the squared circle (in purple) to a position central to stone 23’s centre within the circle, the resulting circle touches the required southern extent of Neal’s rectangle.  The exact displacement is 4³/₈

megalithic yards and the resulting relationship is exactly determined by the use of Pi at 25/8.

More on this will follow as will details of the Carnac Midsummer event as they are announced. See here for next posting on this.

Update on Sunday, March 18, 2007 at 09:58AM by Richard Heath

The squared circle of 40 MY has a perimeter of 125 or 5³ MY and so the square side length must be 5³/2² which is 31.25 MY.  Half of this is 5³/2³ (15+5/8) or 15.625 MY.

Since the circle's radius is 20 MY, then the distance of the new centre, when the circle just touches the base of the rectangle, must be 20 - 15.125 or 4 and 3/8 MY above the rectangle's centre line.

This is the position of the centre of stone 23, shown as a dotted outline by Thom to indicate (I believe) that this was a measurable stone socket in the early 1970's when Thom did his surveying work in Brittany.

As Neal has pointed out, the megalithic yard was probably what is called in metrology a pace, i.e. 2.5 feet of the Drusian variety which at root value is 27/25 feet long, meking a root Drusian pace 2.7 feet long. When varied by 176/175, this becomes 2.7154285:  (the Astronomical Megalithic Yard or AMY). This is a good candidate for the 2.72 foot mean value for the MY found by Thom via statistical analysis of the megaliths in Britain and Brittany (lit. "little Britain").

Other values of the megalithic yard can be found by reducing the yard of Iberian feet (32/35 feet long) which at root is 2.7428571 feet long. Multiplied twice by 175/176, this yard becomes 2.7117776 ft, the Root Least variation suggested by Neal as intended for this aspect of the monument. This system of variation is explained in the Appendix of Sacred Number, also available via the metrology links page. The apparent accuracy of fractions in ancient metrology is an artifact of the fact that the syastem was based upon the prime numbers 2, 3, 5, 7, & 11 whilst decimal notation is based upon just 2 & 5, i.e. 10 [see Prime Numbers in Metrology page].