David Kenworthy has come up with a very intriguing value for the megalithic inch. Forty Megalithic inches go into a Megalithic Yard, according to Alexander Thom's work. David has suggested a value of √2/√3 English inches for the Megalithic inch (or √(2/3), or √6/3, or even √2x√3 / 3 ). In decimal notation, this is 0.81649658 inches, and so consequently there would be 2.7216553 English feet in a Megalithic Yard. This is within the parameters given by Thom. David has documented his findings in these two videos: (102) Academia 6. Solving the Riddle of Pi in the Egyptian Megalithic Yard - YouTube and (102) Academia 4. The Riddle of Alexander Thom's Egyptian Megalithic Yard - YouTube
Why should an irrational value work, and in inches at that? It is probable that what is today the imperial inch has been in existence for a very long time, and originated some time in prehistory. It is certainly not a young unit of measure. Many ancient measures make sense when expressed in inches, or in feet, as John Neal has demonstrated. Why would the square roots of two and three be relevant to a megalithic yard or inch? Many ancient units of measure relate to each other by a so called irrational number (or a transcendental number in the case of pi). As David mentions in his video, Berriman writes that the Egyptian royal cubit is 9 digits multiplied by pi. This works particularly well with an approximation of pi as 22/7, a digit of 0.7291666667" inches, and an Egyptian royal cubit of 20.625". With the value for pi that lives inside a calculator, and with the same digit, you would get a smaller cubit of 20.6167". Berriman points out that the square root of two links the remen to the Egyptian royal cubit, and that pi links six metres to this cubit. It could be that there are other irrational ratios to be found between units of measure, and that we need to look to simple geomtric shapes to get a better understanding of how these units might relate to each other.
What could a unit of √(2/3) or √2/√3 inches mean?
If you take the square root of three in a geometric shape such as the height of a hexagon or an equilateral triangle, with a value of 1, take the side of this hexagon or half the side of this triangle, which will measure 1/√3, and turn it into the side of a square, the diagonal of this square will have a value of √(2/3).
I've used a flower of life as a backdrop to illustrate these ratios.
And here those ratios are coverted to measures based on the value 1 being 1 inch.
If you take the height of the Great Pyramid of Egypt to be 10,000/√3", which is in keeping with Petrie's measure of 5776" (with an allowance of 7 inches either way). Using this height as the side of a square produces a length of 10,000 of these megalithic inches as the diagonal.
Also, if you use the √3 value and multiply it by 6π, you get another slightly different value for the Megalithic Yard in inches: 32.648389. Divided by 40 to produce a megalithic inch, this would be worth 0.8162097". This is slightly different to the √(2/3)" Megalithic inch, because it involves pi. David has put forward a suggestion of √(800/81) for pi. If we use this instead of calculator pi in the √3x6π Megalithic Yard, it reconciles to the √(2/3) Megalithic Yard.
So: √3 x 6 x √(800/81) = 32.65986. as a value in inches, this is the Megalithic Yard. Divided by forty gives precisely √(2/3)".
I think this works really well, and is food for thought about the role of irrational numbers in ancient measure.