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Was Thom misled?
It was at this stage of investigation, that I had the idea that Thom may have been mistaken into thinking that the Circle builders were using integer units of the Megalithic Yard for the radius and Megalithic Rods.for the circumference.
How did Thom measure the stone circles? To establish a Radius, the Diameter must first be determined, and if Thom measured in Feet, then I am prepared to accept his results for the Diameters.
Using Integer units and Half integer units of the Square Root of 3 for the diameter will always produce Integer units of the Megalithic Yard in the Circumferecne, 1/4 and 3/4 of the sqrt 3 unit will produce an extra 1/2 Meg Yard in the Circumference. One doesn't have to know that the unit is sqrt 3,or even the length of it. It is just there when a 1,2,sqrt3 triangle is formed, and as I have said on the previous page the number of Megalithic yards in the circumference divide by 2 is the number of sqrt 3 units in feet in the diameter.
Similarly, Meg Rods in the circumference multiplied by 1 1/4 also gives the diameter in units of sqrt3
Here I must direct you to the admirable website of Tony Crerar who gives a lucid and readable account of Thom and his Circles with plenty of figures and dimensions. .www.megalithicsites.co.uk. (look for '13. Megalithic Mathematics, True Circles).
Unfortunately I cannot agree with his (Thoms) method of 'tweaking' the diameters in order to obtain integrality. It is just not practical.. For instance, to obtain a perimeter of 29 Meg Rods, a 23 MY diameter has been 'tweaked' to a 23.08 MY diameter. Whereas 29 MR * 1 1/4 = 36 1/4 lots of sqrt 3 ft. i.e. 23.0774... MY., and "Hey Presto!", no tweaking required.
The fact that Thom found some stone circles with very near integral units of MY in their diameters, together with integral numbers of Megalithic Rods in their perimeters, was a fortuitous quirk of mathematics.
The one fly in the ointment is that a measure of ONE IMPERIAL FOOT happens to be the basic unit and the key to the controversial Megalithic Yard ..................
........ SOMETHING TO THINK ABOUT !
and one of the result of this thinking, is that 1/2 of any circumference , divided by 2.720699046... , and then multiplied by Sqrt 3, will always equal the diameter of the original circle.
September 2005