## Use of foot ratios in Megalithic Astronomy

The ratios of ancient metrology emerged from the Megalithic innovations of count&compare: counting time as length and comparing lengths as the longest sides of right triangles. To compare two lengths in this way, one can take a longer rope length and lay it out (say East-West), starting at the beginning of the shorter rope length, using a stake in the ground to fix those ends together.

The longer rope end is then moved to form an angle to the shorter, on the ground, whilst keeping the longer rope straight. The Right triangle will be formed when the longer rope’s end points exactly to the North of the shorter rope end. But to do that one needs to be able to form a right angle at the shorter rope’s end. The classic proposal (from Robin Heath) is to form the simplest Pythagorean triangle with sides {3 4 5} at the rope’s end. One tool for this could then have been the romantic knotted belt of a Druid, whose 13 equally spaced knots could define 12 equal intervals. Holding the 5th knot, 8th knot and the starting and ending knots together automatically generates that triangle sides{3 4 5}.

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## Old Yard’s Mastery of the Square Root of 2

The old yard was almost identical to the yard of three feet, but just one hundredth part smaller at 2.87 feet. This gives its foot value as 99/100 feet, a value belonging to a module very close to the English/Greek which defines one relative to the rational ratios of the Historical modules.

So why was this foot and its yard important, in the Scottish megalithic and in later, historical monuments?

If one forms a square with side equal to the old yard, that square can be seen as containing 9 square feet, and each of those has side length 99/100 feet. This can be multiplied by the rough approximation to 1/√ 2 of 5/7 = 0.714285, to obtain a more accurate 1/√ 2 of 99/140 = 0.70714285.

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## Megalithic application of numeric time differences

Natural time periods between celestial phenomena hold powerful insights into the numerical structure of time, insights which enabled the megalith builders to access an explanation of the world unlike our own. When looking at two similarly-long time-periods, the megalithic focussed on the difference between them, these causing the two periods to slide in and out of phase, generating a longer period in which the two celestial bodies exhibit a complete ensemble of variation, in their relationship to each other. This slippage of phase between celestial periods holds a pattern purely based upon number, hidden from the casual observer who does not study them in this way. Such numerical patterns are only fully revealed through counting time and analysing the difference between periods numerically.

For example, the solar year is longer than the lunar year by 10 and 7/8 days (10.875 days) and three solar years are longer than three lunar years by three times 10.875 days, that is by 32 and 5/8th days (32.625 days), which is 32/29 of a single lunar month of 29.53 days.

The earliest and only explicit evidence for such a three year count has been found at Le Manio’s Quadrilateral near Carnac (circa 4,000 BCE in Brittany, France) used the inches we still use to count days, a “day-inch” unit then widespread throughout later megalithic monuments and still our inch, 1/12 of the foot [Heath & Heath. 2011]. The solar-lunar difference found there over three years was 32.625 day-inches, is probably the origin of the unit we call the megalithic yard and the megalith builders appear to have adopted this differential length, between a day-inch count over three lunar and solar years, in building many later monuments.

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