This article is based upon notes made in 22 May 2014 whilst the 32/29 relationship between AMY and day-inch lunar month was discovered by autumn 2009 (after this paper), being driven to use day-inch counting to explain the origins of megalithic monuments evidently created in the pursuit of astronomical knowledge yet measuring time as lengths. The movement from counting days as inches to using megalithic yards to stand for lunar months was partly explained in my Sacred Number and the Lords of Time by the fact that the excess of lunar months in the solar year is 7/19ths of a lunar year, a residue which adds up over nineteen years to lead to the Metonic period having 235 lunar months in nineteen years. If the AMY is 19/7 feet then it cancels with the residue if and when the megalithic astronomers counted in lunar months.Until last year, there seemed no way to derive the astronomic megalithic yard short of a Metonic scale of monument but the work on this site, on numeracy, and a growing set of techniques such as scaling, proportioning to cancel factors from denominators and hence "clear" fractions, has revealed the 32/29 relationship as deducible in the megalithic and necessary for the quantification of N = 32.585 inches, the measure Robin Heath refers to as the astronomic megalithic yard.

Le Manio's Quadrilateral

This unique monument (figure 8), located east of the Carnac Alignments, has been interpreted as being a kerb monument, possibly once filled in as a mound. However, the kerbs follow a very purposeful geometrical design and have a south west to north east diagonal equal to four solar years in day-inch counting. The southern kerb (figure 1) expresses three years from a sun gate (a backsight for both summer and winter solstice sunrises), of two types - three lunar years and three solar years. The relations between these is then projected into the Quadrilateral as a right angled triangle (figure 2). The astronomers at Carnac appear to have understood the right angled triangle as a means to define the ratio (or interval) between time periods as a super-particular ratio of the form N (the base) to N+1 (the hypotenuse), as well as enabling units of measure to be reproportioned in order to "clear" the residues in their measures (that we call fractions.) Fractions can be avoided by choosing units of measure which divide into a measured distance a whole number of times. But in order to achieve this, the whole of a given problem had to be matched with different parts of their toolkit: metrological triangles. Instead we would flatten such problems into arithmetical solutions, and can ignore fractions by using the decimal system. 


3 4 QUAD Sillouette SIMPLE

Figure 1 The sillouette of the southern kern of Le Manio's Quadrilateral made from a photo survey by the author.The stones are numbered from the Sun Gate, see below, and reach three lunar years at Q atop stone 36 and three solar years at Q' at eastern end of stone 37. See plan in figure 2 and photo of "gate".

In Stone Circle Design and Measurement, G J Bath says

The Ancient Egyptians developed a procedure to determine the area of a circle by subtracting one-ninth from the diameter and squaring the result. 

This can be best visualised as:

CircleFromSquare equalarea

Figure 1 The near integer relationship between the half side length of a square and the circle of equal area.

Generative Properties of the Square Circle and Cube