These are some sections I prepared for the (contested) Megalithic Yard page on Wikipedia. This is part of an effort to defend the historical development of this measure (first proposed by Alexander Thom) from scientific attempts to "airbrush it out of history", along with Thom's role in surveying Britain's monuments for posterity.
Firstly, the arguments for a geometrical origin need to be presented and I have placed this on the Wikipedia page today.
Secondly, I cannot add my own contribution, with Robin Heath, in which the megalithic yard is seen as likely to be derived from a differential day count between three solar and three lunar years, conducted in one inch per day and evident in the Quadrilateral at Le Manio.
Thirdly, Colin Renfrew's 2010 compendium on measure within archaeology has an article in which Japanese researcher Saburo Sugiyama, after decades of working with new survey data, has found a unit identical to the megalithic yard [83cm], at the city of Teotihuacan in the Mexico Basin, called a TMU or Teotihuachan measurement unit. It is quite typical for such work to not research old world historical metrology since there is a scientific ban on theories that Amerindian traditions might have derived partly through ideas from both the Pacific Asian and Atlantic European systems of ocean currents and prevailing winds.
Arguments for a Geometric Derivation
Some commentators upon Thom's megalithic yard (John Ivimy and then Euan Mackie) have noted how such a measure could relate to geometrical ideas found historically in two Egyptian metrological units; the remen of about 1.2 feet and royal cubit of about 1.72 feet. The remen and royal cubit were used to define land areas in Egypt: "On documentary and other evidence Griffith came to the conclusion that the square on the royal cubit was intended to be twice that the square on the remen; and Petri identified the remen as a length of 20 digits" .
Explains how some have derived Thom's
Megalithic Yard unit of measure
from metrological land measure relationships
established historically in Egypt's Dynastic periods
A square with side length equal to the diagonal of a square with side length equal to one remen has an area of one square royal cubit, ten thousand (a myriad) of which defined an Egyptian land measure, the setat. [cite mackie] John Ivimy noted that "The ratio MY : Rc is SQRT(5) : SQRT(2) to the nearest millimeter, which makes the MY equal to SQRT(5) remens, or the length of a 2 x 1 remen rectangle." ), see figure below
The main weakness in this argument is probably that the builders of the megalithic would have needed the remen and royal cubit, upon which this geometrical relationship relies numerically, to derive their yard.~~RichardDHeath~~
Possible Astronomical Origins
There is a simple explanation for the existence of the megalithic yard as being important to Megalithic Astronomy, if that astronomy counted days using a standard unit. The found difference between three solar years [1095.75 days] and three lunar years [1063.1 days] is 32 and five eighths of a day, which lies within the numeric range of the megalithic yard in inches, if valued at 2.72 feet long.
In 2010, a monument was found [Le Manio Quadrilateral] near Carnac, in which a three year count is to be found expressed in day-inches, using a right triangle between the summer solstice sunrise alignment and a long kerb of 36 to 37 stones, the number of lunar months over three years of either sort.
Since the inch is still a current unit of length, this implies that the thumb's breadth was simply standardised in the terminal Paleolithic, which was already counting days, lunar months and years according to Alexander Marshack. Adopting a standard length per day enabled the comparison of different lengths of time, using a then calibrated geometry of the right triangle.~~RichardDHeath~~ for review
As Architectural Unit in Pre-Columbian Mexico
Alexander Thom's megalithic yard emerged because he sought the type of metrological unit necessary for building large and complex buildings, which some megalithic structures are. A recent similar effort was made to find the principle unit of measure employed when building some or all stages of the pre-Columbian City of Teotihuacan, in the Basin of Mexico.
In Colin Renfrew's compendium The Archaeology of Measurement, Saburo Sugiyama published Teotihuacan city layout as a cosmogram (page 130). He had previously studied (1983) the dimensions within the Feathered Serpent Pyramid [FSP]. He says "my search for the TMU [Teotihuacan Measurement Unit] began at the main sculpted façade of the FSB" and "These data from the FSB led me to suggest that a unit of 83 cm was used at Teotihuacan". His TMU of 83 cm [2.723 feet] is very close to the nominal length given by Thom for the megalithic yard as 2.72 feet (see above).
Sugiyama then proposed in The Archaeology of Measurement that many lengths within the city relate to the Maya calendar, the astronomical period called the eclipse year [of 346.62 days] and sacred calendric period the Tzolkin [of 260 days]. For example, on page 144, figure 11.9, he deduces a distance between the centres of the FSP and Sun Pyramid based on the survey by Million et al.  as being 1194.99 m which would be 1439.75 (probably 1440) of his TMU of 83 cm. Some other definable lengths within the city gave similar numerical results of nearly-whole and significant numbers of TMUs. He thus suggests a unit equal to the megalithic yard was used in pre-Columbian Mexico, though Sugiyama sees no parallel between his TMU and the megalithic yard.~~RichardDHeath~~ for review