## How Geometries transformed Time Counts into Circles

Above: example of the geometry that can generate one or more circles,
equal to a linear time count, in the counting units explained below.

It is clear, one so-called “sacred” geometry was in fact a completely pragmatic method in which the fourfold nature of astronomical day and month counts allowed the circularization of counts, once made, and also the transmission of radius ropes able to make metrological metrological circles in other places, without repeating the counting process. This “Equal Perimeter” geometry (see also this tag list) could be applied to any linear time count, through dividing it by pi = 22/7, using the geometry itself. This would lead to a square and a circle, each having a perimeter equal to the linear day count, in whatever units.

And in two previous posts (this one and that one) it was known that orbital cycles tend towards fourfold-ness. We now know this is because orbits are dynamic systems where potential and kinetic energy are cycled by deform the orbit from circular into an ellipse. Once an orbit is elliptical, the distance from the gravitational centre will express potential energy and the orbital speed of say, the Moon, will express the kinetic energy but the total amount of each energy combined will remain constant, unless disturbed from outside.

In the megalithic, the primary example of a fourfold geometry governs the duration of the lunar year and solar year, as found at Le Manio Quadrilateral survey (2010) and predicted (1998) by Robin Heath in his Lunation Triangle with base equal to 12 lunar months and the third side one quarter of that. Three divides into 12 to give 4 equal unit-squares and the triangle can then be seen as doubled within a four-square rectangle, as two contraflow triangles where the hypotenuse now a diagonal of the rectangle.

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## The Octon of 4 Eclipse Years

Having seen, in the last post, that three eclipse years fitted into the three-year count at Le Manio, another eclipse fact has come to light, recorded within the nearby site of Crucuno, between its dolmen and rectangle. The coding of time at Crucuno was an evolution of a new metrology based upon the English foot in which, the right triangle of longest integer side lengths was replaced by fractions of a foot using the same two numbers as the sides would have had. This allowed the measurement of a time period to be simultaneously seen in both days and months. That this was possible can be seen at Le Manio, where it could be noticed that 32 lunar months equaled exactly 945 day-inches.

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## The Quantification of Eclipse Cycles

Following on from the last post:
Given the many sub-cycles found in the Moon’s behavior, and the angle of its orbit to the Ecliptic, one would expect the eclipse phenomenon to be erratic or random but in fact eclipses repeat quite reliably over relatively fixed periods that were quantified symbolically by megalithic astronomy, within monuments and by the “sacred” numbers and geometries which encapsulate eclipse cycles, as with many other cycles.

An eclipse cycle repeats, to greater or lesser degree of accuracy, over an integer number of days or months. And because of a lack of conventional arithmetic or notation like our own in the megalithic, the practical representation of a cycle would be a raw count of days or months, using uniform measures, which could then be interpreted by them using (a) the rational fractions of whole unit metrology, (b) the factorization of a measured length by counting within using measuring rods or (c) using right-triangles or half-rectangles, which naturally present trigonometrical ratios; to compare different time cycles.

## The Eclipse Year

The solar year (365.242 days) is longer than the lunar year of 12 lunar months (354.367 days) and we know that these, when counted in day-inches, gave the megalithic their yard of 32.625 (32 and 5/8) inches and that, by counting months in megalithic yards over one year, the English foot (of 12 inches) was instead the excess over a single lunar year of the solar year, of 12.368 lunar months. 0.368 in our notation is 7/19 and the megalithic yard is close to 19/7 feet so that counting in months cancels the fraction to leave one foot.

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## The Fourfold Nature of Eclipses

The previous post ended with a sacred geometrical diagram expressing the eclipse year as circumference and four anomalous months as its diameter. The circle itself showed an out-square of side length 4, a number which then divides the square into sixteen. If the diameter of the circle is 4 units then the circumference must be 4 times π (pi) implying that the eclipse year has fallen into a relationship with the anomalous month, defined by the moon’s distance but visually by manifest in the size of the moon’s disc – from the point of view of the naked eye astronomy of the megalithic.

In this article I want to share an interesting and likely way in which this relationship could have been reconciled using the primary geometry of π, that is the equal perimeter model of a square and a circle, in which an inner circle of 11 units has an out-square whose perimeter is, when pi is 22/7, 44.

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