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Megalithic Mathematics 4

The 'D' rings. 3.4.1  Thom discovered over thirty examples of a class of megalithic stone rings he termed 'flattened' or 'D' rings. These designs exhibit two methods, (type A and type B), of reducing the length of the perimeters of the rings in ratio to the diameters. In both these approaches the perimeters are, sensibly, exact multiples of 3 times the diameters- perhaps an attempt to rationalise pi and eliminate an incommensurable.

A.Thom, Megalithic Sites in Britain p.28.

pi  for this design = 3.0591

	3.4.2  Type A construction. Following is a six part instruction set for the construction of a D ring type A. Using this procedure the ring could be drawn on the ground using only a rope and pegs

3.4.3  In most of the true circles and rings the construction lines and points have been removed leaving only the perimeters outlined in large stones, however at several sites the centres of the designs or the auxiliary centres such as E and F or the junctions of arcs on the perimeter have been marked by small recumbent stones. These small markers are always to one side of the exact position. A clear example of construction point marking can be seen at Kerry Pole3.7.2 stone ring in Montgomeryshire, Mid Wales. The centre of this design and eight other construction points are indicated.

3.4.4  Histogram of D rings type A. The following data on the dimensions of the surveyed D type A rings has been extracted from Thom's original Fig. 5.1 page 46 of Megalithic Sites in Britain.

Derived from A.Thom, Megalithic Sites in Britain p.46.

3.4.5  Astronomically orientated rings. Thom believed that one of the important motivations for the development of the complex rings was to provide more opportunities to fit a geometric shape to the constraints of astronomical alignments emanating from unique positions in the landscape. The numerous construction lines allowed more chances of matching directions to significant foresights on the horizon. Many instances have been found where two or more principal lines are aligned with Megalithic Calendar foresights and the north/south meridian. For details of an astronomically orientated D ring type A see html page Brook Cottage Henge.

	3.4.6  Type B construction. pi  for this design = 2.9572 Following is a six part instruction set for the construction of a D ring type B. Using this procedure the ring could be drawn on the ground using only a rope and pegs

Again this design may be drawn using only rope and pegs. The initial trisection of the main diameter can be achieved by folding a rope of the diameter length into three parts.

Derived from A.Thom, Megalithic Sites in Britain p.46. Again the diameters are given, in the top line, in Megalithic Yards and the perimeters, lower, in Megalithic Yards and the nearest integer of Megalithic Rods.

	3.4.7  Two examples; Rough Tor and Dinnever Hill. To test Thom's assertions of both the D ring geometry and the integral metrical formula larger rings consisting of many small stones should show the situations more precisely than rings built with larger stones. Here are high precision digital examinations performed upon two site plans taken from Megalithic Sites in Britain.

3.4.8  Dinnever Hill S1/8. From a precise template three D type A rings, two coloured red and one black, have been layered on top of Thom's survey of Dinnever Hill stone ring. The two rings, at 62 & 63 Megalithic Rods, are the nearest with perimeters expressed in whole Megalithic Rods. A very good match to the geometry of D type A is clear. However neither of the two layered rings have diameters close to integrality in Megalithic Yards. The diameters are 51.49 and 50.67 MY. If the 60 MR perimeter had been chosen the necessary diameter would be 49.03 MY - a near perfect solution to the demands of the MR/MY formula for rings theorised by Thom. Why was this conveniently near 60 MR ring not chosen at Dinnever Hill?

Based on plan in A.Thom, Megalithic Sites in Britain p.58.

3.4.9  Rough Tor S 1/7. An accurate template for the ring with the 69 MR perimeter has been layered onto the plan for the stones at Rough Tor. This gives very satisfactory matching to a variation of the D type A ring. This ring strikes the shoulder arcs from a centre one third of the length of a radius instead of one half. Also the major diameter is within 0.07 MY of the perfect nominal 56 MY.

Based on plan in A.Thom, Megalithic Sites in Britain p.57.

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