Geometry 2: Maintaining integers using fractions

understanding the megalithic: circular structures: part 2

The megalithic sought integer lengths because they lacked the arithmetic of later millennia. So how did they deal with numbers? There is plenty of evidence in their early monuments that today’s inch and foot already existed and that these, and other units of measure, were used to count days or months. From this, numbers came to be known by their length in inches and later on as feet, and longer lengths like a fathom of five feet, the cubit of 3/2 feet and, larger still, furlongs and miles – to name only a few.

So megalithic numeracy was primarily associated with lengths, a system we call metrology. Having metrology but not arithmetic, the integer solutions to problems became a necessity. Incidentally, it was because of their metrological numeracy that the megalithic chanced upon a rich seam of astronomical meaning within the geocentric time world that surrounds us, a seam well-nigh invisible to modern science. Their storing of numbers as lengths also led to their application to the properties geometrical structures have, to replicate what arithmetic and trigonometry do, by using right triangles and a system of fractional measures of a foot (see later lesson – to come). In what follows, for both simplicity and veracity, we assume that π was too abstract for the megalithic, since they first used radius ropes to create circles, so that 2π was a more likely entity for them to have resolved.

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Geometry 1: π

understanding the megalithic: circular structures: part 1
What is the relationship of a circles perimeter to its width, called its “diameter”?

It would require 3 and a bit diameters to wrap around the circle – the ratio of 3 and a bit diameters to the perimeter is known as “Pi”, notated by the Greek symbol “π”. Half of the diameter, from the circle’s center to its edge, is named its radius.

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paper: Lunar Simulation at Le Manio

Our survey at Le Manio revealed a coherent arc of radial stones, at least five of which were equally long, equally separated and set to a radius of curvature that suggested a common centre. It appears the astronomers at Le Manio understood that, following three lunar sidereal orbits (after 82 days) the moon would appear again at the same point on the ecliptic at the same time of day

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 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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Chalk Drums to Symbolise Pi and Layout Monuments

December 2016 in Hits: 3872

Three Folkton Chalk Drums found in a young girl’s grave
©Trustees of the British Museum ]

Perhaps as early as 4000 BC, there was a tradition of making chalk drums. Three highly decorated examples were found in a grave dated between 2600 and 2000 BC in Folkton, northern England and one undecorated chalk drum in southern England at Lavant in an upland downs known for a henge and many other neolithic features discovered in a recent community LIDAR project. The Lavant LIDAR project and the chalk drum found there are the first two articles in PAST, the Newsletter of The Prehistoric Society. (number 83. Summer 2016.) It gives the height and radius of both the Folkton drums 15, 16 and 17 and the Lavant drum, presenting these as a graph as below.

Adapted graphic showing diameters in inches (above in red) as well as mm, and the possible PI relationships for the chalk drum diameters, key to the fact that such drums can be rolled. In line with megalithic numeracy, the simple yet accurate value of 22/7 for PI is shown.
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