Category: Sacred Geometry: Language of the Angels

Released in January 2021, this book explores sacred building as the continuation of the megalithic: its astronomical knowledge, geometrical and metrological methodology and knowledge of the size of the Earth. The megalithic was our first numerate culture which discovered the main design design parameters for our existence, organised by higher intelligences called angels.

Geometry 5: Easy application of numerical ratios

above: Le Manio Quadrilateral

This series is about how the megalithic, which had no written numbers or arithmetic, could process numbers, counted as “lengths of days”, using geometries and factorization.

My thanks to Dan Palmateer of Nova Scotia
for his graphics and dialogue for this series.

The last lesson showed how right triangles are at home within circles, having a diameter equal to their longest side whereupon their right angle sits upon the circumference. The two shorter sides sit upon either end of the diameter (Fig. 1a). Another approach (Fig. 1b) is to make the next longest side a radius, so creating a smaller circle in which some of the longest side is outside the circle. This arrangement forces the third side to be tangent to the radius of the new circle because of the right angle between the shorter sides. The scale of the circle is obviously larger in the second case.

Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius. diagram of Dan Palmateer.

Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius.

Continue reading “Geometry 5: Easy application of numerical ratios”

Geometry 4: Right Triangles within Circles

This series is about how the megalithic, which had no written numbers or arithmetic, could process numbers, counted as “lengths of days”, using geometries and factorization.

My thanks to Dan Palmateer of Nova Scotia
for his graphics and dialogue for this series.

This lesson is a necessary prequel to the next lesson.

It is an initially strange fact that all the possible right triangles will fit within a half circle when the hypotenuse equals the half-circles diameter. The right angle will then exactly touch the circumference. From this we can see visually that the trigonometrical relationships, normally defined relative to the ratios of a right triangle’s sides, conform to the properties of a circle.

A triangle with sides {3 4 5} demonstrates the general fact that, when a right triangle’s hypotenuse is the diameter of a circle, the right angle touches the circumference.
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Geometry 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
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A Pyramidion for the Great Pyramid

image: By 1200 BC, the end of the Bronze Age, the Egyptian map of the world (above) showed nine bows or latitudes, numbers 4 to 9 including the Nile Delta, Delphi, Southern Britain and Iceland, a map based on an ancient geodetic survey.

This post explores a pyramidion, now lost, which exceeded the apex height of the pyramid, so as to model the different reference latitudes established by geodetic surveys and encoded within their metrology and the Great Pyramid (by 2500 BC). This pyramidion would have sat on the flat top of the pyramid, 480 feet above the base of the pyramid.

In All Done With Mirrors, John Neal described how the full height of the pyramid, reaching to its natural apex, would have been just over 481 feet. Most pyramids probably had a pyramidion since a number have been found elsewhere that repeat aspects of or have a name carved on them, of a specific pyramid. Sitting on their apex, they often repeat the form of the larger pyramid, and are scale models of a specific pyramid. In the case of the Great Pyramid, exactly 441th of its natural apex is missing, and this is likely to be because a pyramidion once stood on the flat top the actual pyramid.

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Recalibrating the Pyramid of Giza

Once the actual height (480 feet) and actual southern base length (756 feet) are multiplied, the length of the 11th degree of latitude (Ethiopia) emerges, in English feet, as 362880 feet. However, in the numeracy of the 3rd millennium BC, a regular number would be used. In the last post, it was noted that John Neal’s discovery of such rectangular numbers to define degrees of latitude, multiplied the pyramid’s pointed height (481.09 feet) by the southern base length (756 feet) to achieve the length of the Nile Delta degree of latitude and, repeating Neal’s diagram relating the key latitudinal degrees of the ancient Model as figure 1, the Ethiopian degree is 440/441 of the Nile Delta degree. As shown above, the length of the 756 foot southern base is changed, when re-measured in the latitudinal feet for Ethiopia; it becomes the harmonic limit of 720 feet of 1.05 feet – normally called the root Persian foot.

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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.