Lesson 3: Making a circle from a counted length

The number of days in four years is a whole number of 1461 days if one approximates the solar year to 365¼ days. This number is found across the Le Manio Quadrilateral (point N to J) using a small counting unit, the “day-inch”, exactly the same length as the present day inch. It is an important reuse of a four-year count to be able to draw a circle of 1461 days so that this period of four years can become a ouroboros snake that eats its own tale because then, counting can be continuous beyond 1461 days. This number also permits the solar year to be counted in quarter days; modelling the sun’s motion within the Zodiac by shifting a sun marker four inches every day.

Figure 1 How a square of side length 11 will equal the perimeter of a circle of diameter 14

Our goal then is to draw a circle that is 1461 day-inches in perimeter. From Diagram 1 we know that a rope of 1461 inches could be divided into 4 equal parts to form a square and from that, an in-circle to that square has a diameter equal to a solar year of 365¼ days. Also, with reference to Figure 1, we know that the out-circle will have a diameter of 14 units long relative to the in-circle diameter being 11 units long, and this out-circle will have the perimeter of 1461 inches that we seek.

Figure 3 A general method, using the equal perimeters model, applied to a 4 solar year day count of 1461 day-inches, found as a linear count at the Manio Quadrilateral. A square, formed from this linear count, can be transformed into an outer circle of equal perimeter using the simple geometry of π as 22/7.

For this, the solar year rope (the in-circle diameter) needs to be divided into 11 parts. Start by choosing a number that, when multiplied by 11, is less that 365 (and a 1/4). For instance, 33. A new rope will be formed, 11 x 33 = 363 inches, marked every 33 inches to provide 11 divisions. Through experience, we discover we need 2 identical ropes so as to make practical use of the properties of symmetry through attaching ropes to both ends of the solar diameter rope.

Place one rope at the West side of the in-circle diameter and swing it up until it touches the in-circle. Place the other rope at the East side of the in-circle diameter and swing it down until it touches the edge of the in-circle. Now connect the 33 inch marks between the 2 ropes. This will divide the 365 1/4 diameter into 11 segments.

Seven of those segments are the new radius to create the 1461 inch outer-circle.

Figure 3 Division of the in-circle into eleven equal parts so as to select 7 units as a radius rope to then form the circle of diameter 14 units and perimeter 1461 inches.

This novel application of the equal perimeters model, rescued from Victorian textbooks by John Michell and applied by him most memorably perhaps to Stonehenge and the Great Pyramid (in Dimensions of Paradise) is a general method for taking a counted length and reliably forming a radius rope able to transform that counted length into a circle of the same perimeter as the square, easily formed by four sides ¼ of the desired length.

The site survey at the start, drawn by Robin Heath, appeared in our survey of Le Manio.

paper: The Origins of Day-Inch Counting

ABSTRACT
This paper presents the theory that in the Megalithic period, around 4500-4000 BCE, astronomical time periods were counted as one day to one inch to form primitive metrological lengths that could then be compared, to reveal the fundamental ratios between the solar year, lunar year, and lunar month and hence define a solar-lunar calendar. The means for comparison used was to place lengths as the longer sides of right angled triangles, leading to a unique slope angle. Our March 2010 survey of Le Manio supports this theory.

82: A Natural Accurate Pi related to Megalithic Yard

Author at Le Manio Quadrilateral (c. 4000 BC) in 2010. To left, the end of the southern-kerb’s day-inch count, which created the first megalithic yard of 261/8 (32.625) day-inches.

In my academia.edu paper on lunar simulators, based upon the surviving part of a circular structure at Le Manio (Carnac, Brittany), a very simple but poor approximation to PI could be assumed, of 82/26 (3.154) since there seem to have been 82 stones in the circle and the diameter was 26 of the inter-stone distance of 17 inches. The number 82 is significant to simulation of the moon’s orbit since that orbit is very nearly 27 and one third days long (actually 27.32166 days). In three orbits therefore, there are almost exactly 82 days and in day-inch counting that is 82 day-inches. Also of interest is the fact that in three orbits, the exact figure would be 81.965 day-inches which approaches the megalithic rod of 2.5 MY as 6.8 feet.

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Astronomical Time within Clava Cairns

In North East Scotland, near Inverness, lies Balnuaran of Clava, a group of three cairns with a unique and distinctive style, called Clava cairns; of which evidence of 80 examples have been found in that region. They are round, having an inner and outer kerb of upright stones between which are an infill of stones. They may or may not have a passageway from the outer to the inner kerb, into the round chamber within. At Balnuaran, two have passages on a shared alignment to the midwinter solstice. In contrast, the central ring cairn has no passage and it is staggered west of that shared axis.

This off-axis ring cairn could have been located to be illuminated by the midsummer sunrise from the NE Cairn, complementing the midwinter sunset to the south of the two passageways of the other cairns. Yet the primary and obvious focus for the Balnuaran complex is the midwinter sunset down the aligned passages. In fact, the ring cairn is more credibly aligned to the lunar minimum standstill of the moon to the south – an alignment which dominates the complex since, in that direction the horizon is nearly flat whilst the topography of the site otherwise suffers from raised horizons.

Cairns at Balnuaran of Clava. plan by A. Thom and pictures by Ian B. Wright
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Three Lunar Orbits as 82 day-inches

Sacred Number and the Lords of Time interpreted Thom’s megalithic fathom of 6.8 feet (as 2.72 feet times 2.5) found at Carnac’s Alignments as a useful number of 82 day-inches between stones in the stone rows of Le Menec. After 82 days, the moon is in almost exactly the same place, amongst the stars, because its orbit of 27.32166 days is nearly 27 and one third days. Three orbits sums to nearly 82 days. But the phase of the moon at that repeated place in the sky will be different.

The stone rows of Le Menec are not straight and in places resemble the deviations of the lunar nodes seen in late or early moon rise or setting phenomenon.
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