Use of Ad-Quadratum at Angkor Wat

The large temple complex of Angkor Wat ( photo: Chris Junker at flickr, CC BY-NC-ND 2.0 )

Ad Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root
of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).

The diagonal of a square of unit size is sqrt(2), When a square is nested to just touch a larger square’s opposite sides, one can know the squares differ by sqrt(2)
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The Three Worlds at Gavrinis

following on from previous post,
an article by M Guillaume found in
AAK Etudes et Travaux No. 1, 1977

Do these three stages [at Gavrinis] not correspond to the three creations, probably inherited by Celts, and  those in Egypt, preceding access to a sanctuary?

Fig. 10 Top left: A tracing of the Druid worlds, the circle in the square defining three areas: Abred (circle of necessity) and Annouim and Gwenwed (the white world). Top right:  On the stone Suèvres, these worlds are the figures by concentric squares. Bottom: In Christianity we find the same structure: this rose at Chartres has a fourth inner circle.
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Gavrinis: On Crossing the Three Thresholds and Entering The Room

following on within an article by M Guillaume found in AAK Etudes et Travaux No. 1, 1977

These half-circles facing upwards – do we not find them repeated a thousand times in the “necklaces” of the Goddess?

Fig. 12 Stones 4 and 5
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Symbolic “forms in movement” at Gavrinis

In this article M.Guillaume introduces some of the AAK’s work on understanding the Gavrinis chambered cairn. It appeared in the first volume of Etudes et Travaux, May 1977, pages 45-51.

It has been translated from French as best I can, in three parts with links between. It was first re-published on the web between 2010-2012 to honour the fact I was given copies of the magazine when visiting Carnac in 2004.

Whilst my interest was site interpretation using numbers, the notion of a vision quest within Gavrinis as an experienced structure is appealing.

What especially strikes one on entering Gavrinis is the extreme  homogeneity of the whole work.

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Gavrinis 1: Its dimensions and geometrical framework

This article first appeared in my Matrix of Creation website in 2012 which was attacked, though an image had been made. Some of this material appeared in my Lords of Time book.

photo For Wikipedia by Mirabella.

Gavrinis and Tables des Marchands are very similar monuments, both in the orientation of their passageways and their identical latitude. Gavrinis is about 3900 metres east of Tables des Marchands but, unlike the latter, has a Breton name based upon the root GVR (gower). Both passageways directly express the difference between the winter solstice sunrise and the lunar maximum moonrise to the South, by designing the passages to allow these luminaries to enter at the exact day of the winter solstice or the most southerly moonrise over many lunar orbits, during the moon’s maximum standstill. Thus both the monuments allow the maximum moon along their passageway whilst the winter solstice sunrise can only glance into their end chambers.

From Howard Crowhurst’s work on multiple squares, we know that this difference in angle is that between a 3-4-5 triangle and the diagonal of a square which is achieved directly by the diagonal of a seven square rectangle.

Figure 1 The essence of difference between the winter solstice sunrise (as diagonal of 4 by 3 rectangle) and southerly maximum moonrise (as diagonal of a single square), on the horizon, is captured in the diagonal of a seven squares rectangle.
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The Golden Mean compared to PI

In reviewing some ancient notes of mine, I came across an interesting comparison between the Golden Mean (Phi) and PI. They are more interesting in reverse:

A phi square (area: 2.618, side: 1.618) has grown in area relative to a unit square by the amount (area: 0.618) plus the rectangle (area:1 ). This reveals the role of phi’s reciprocal square (area: 0.384) in being the reciprocal of the reciprocal so that in product they return the unity (area: 1).

On the right, the phi squared square showing how the reciprocal of phi and its square uniquely sum to unity (area: 1), a property that is scale invariant between structures who share the same units and grow according to the Golden Mean.
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