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.

Figure 1 Forming a Square with the Old Yard. The diagonal of the foot squares is then 7/5, the simplest approximation to √ 2.
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Models of Time within Henges and Circles

image: composite, see figure 1 below

Presenting important information clearly often requires the context be shown, within a greater whole. Map makers often provide an inset, showing a larger map at a smaller scaling (as below, of South America) within a detailed map (of Southern Mexico).

This map is shown in the context of South America with a yellow rectangle which is the part blown up in scale. The subject is the Quetzal birds range which corresponds well to the Olmec then Maya heartlands leading to the god named Quetzalcoatl or Feathered Serpent. (see chapter 8 of Heath, 2018.)

Megalithic astronomy generated maps of time periods, using lines, triangles, diameters and perimeters, in which units of measure represented one day to an inch or to a foot. To quantify these periods, alignments on the horizon pointing to sun and moon events were combined with time counting between these events,where days, accumulated as feet or inches per day, form a counted length. When one period was much longer than another, the shorter could be counted in feet per day and the smaller in inches per so that both counts could share the same monumental space. In this article we find the culture leading to megalithic astronomy and stone circles, previously building circular structures called henges, made of concentric banks and ditches.

Thornborough Henge
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Harmonic Earth Measures

The Size of the Earth’s Meridian

It appears the ancient world had unreasonably accurate knowledge of the size of the earth and its shape: Analysis of ancient monuments reveals an exact estimate for the circumference of the mean Earth, a spherical version of the Earth, un-deformed by it spinning once a day. Half of this circumference, the north-south meridian, was known to be about 12960 miles (5000 geographical Greek feet of 1.01376 ft), a number which (in those Greek units) is then 60^5 = 777,600,000 geographical Greek inches. One has to ask, how such numbers are to be found very accurately within a planet formed accidentally during the early solar system?


Figure 1 The Earth as a circular Equator and a spherical Mean Earth, whose half circumference approximates the non-circular distance between north and south poles

John Michell’s booklet on Jerusalem found (in its Addendum) that the walls of the Temple Mount, extended for the rebuilding of the Temple of Solomon, was a scaled down model of the mean-earth Meridian in its length. These walls are still 5068.8 feet long, which is the length of a Greek geographical mile. This unit of measure divides the meridian into 12960 parts, each a geographical Greek mile.

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