The Fibonacci series is an ideal pattern, widely found within living systems, in which the present magnitude or location of something is the product of two previous magnitudes or locations of it. The next magnitude will again be the sum of the last two magnitudes in what is, an algorithmic pattern producing approximation to the Golden Mean (designated by the Greek letter φ,’phi’). As the series gets larger, the ratio (or proportion) between successive magnitudes will better approximate the irrational value of φ = 1.618033 … – which has an unlimited fractional part whilst the virtue of the Fibonacci numbers within the Series is that they are integers forming rational fractions.

Continue reading “Fibonacci in Jupiter’s 12-fold Heaven”## The Avebury Square within it’s Southern Circle

Soil resistance work (“geophys”), by archaeologists from the University of Leicester, of the land inside the southern stone circle of Avebury Henge, has revealed more about the Obelisk and lines of standing stones, which appear to have formed a near-square rectangle. Information can be hard to obtain when work is yet to be published but a press release to the Guardian and others many months ago (December 27th 2019) enabled figures from a media set to be viewed with public access. This has enabled me to so some site interpretation, using the (as-yet damned) numerical technique called ancient metrology. My results are fascinating and build upon the megalithic use of counting time as length to track important time-cycles such as the Nodal Period of 6800 days, between lunar maxima and minima, and the Metonic period of both 19 years and 235 lunar months, within which all of the varied orientations of Sun Moon and Sky are recycled.

Continue reading “The Avebury Square within it’s Southern Circle”## Use of Ad-Quadratum at Angkor Wat

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).

## Silbury Hill: Metrological Key to the Model of the Earth between Stonehenge & Avebury

#### Archived: **11 August 2012**

The exact location of Silbury Hill is as mysterious as the purpose of the Hill itself, a thirty degree cone, only recently with a flat top, overlooking Avebury and the surrounding hills. The Hill figures in **John Michell’s model of the Earth between Stonehenge and Avebury** in which one quarter of a degree of latitude, between the two henges, appears to have been measured by a type of Persian foot so as to make the number of feet, in between, equal numerically to that required to perfectly model the Earth using 864:866:867 double triangle.

There are **86400 Persian feet** of 1.056 feet (south to north) between Stonehenge and Avebury Ridgeway enabling the Avebury henge to be 86600 of these Persian feet from Stonehenge, then to represent the Mean Earth radius (see Initial Article – *missing link*). The Avebury henge appears to have been specifically tied to the distinct Latitude of 360/7 degrees.

## 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.

Continue reading “Symbolic “forms in movement” at Gavrinis”## The Crop Circle Phenomenon at Crooked Soley

#### Archive: 26 November 2017

This article explores another modern and highly transient manifestation belonging to the category of **Landforms**, the crop circle. Thought in seventeenth century England to be the work of a mowing devil, and more recently hoaxers, the large crop fields created since the post-war tractor revolution play host to “sacred art” designs that farmers find intrusive, attracting members of the public (to be a-mazed) and aviators to curate these patterns for posterity. The tabloids used to indulge full page colour sections to crop circles but then were dissuaded perhaps by officialdom (we are mad) and apathy (we lose interest) since the cause of the finest examples, such as Crooked Soley, do not appear humanly possible.

## Film of John Michell at Lundy Island

This is a film by me of John Michell before his death. It was made on Lundy Island at which time he was working on some of his last published ideas about the British Isles from the perspective of sacred geometry and metrology, both fields in which John made outstanding contributions including *The View Over Atlantis*, *Dimensions of Paradise* and *Ancient Metrology*. It is published here to enable those who did not to experience the unique presence of John Michell, itself conducive to understanding his work.

originally published Monday, 28 May 2012 at 10:58

It was read **478** times

## 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.

* Gavrinis *and

*are very similar monuments, both in the*

**Tables des Marchands****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**.

## 82: A Natural Accurate Pi related to Megalithic Yard

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.

Continue reading “82: A Natural Accurate Pi related to Megalithic Yard”## Form implied by the Kaaba’s Walls

The Kaaba appears to express a geometrical progression of adjacent odd numbers starting with one and three. This differs from the super-particular ratios found within the right triangles of astronomical time periods formed by the Megalithic, in which the ratio pairs separated by only one rather than by two, between only odd numbers. However, the multiple-square rectangles used by the megalithic to approximation celestial ratios, made use of the three-square rectangle. In one of the smallest of these rectangles, it simultaneously approximates two pairs of ratios: The eclipse year (346.62 days) to the solar year (365.2422 days) and the solar year to the thirteen lunar month year (384 days).

Continue reading “Form implied by the Kaaba’s Walls”## 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).

Continue reading “The Golden Mean compared to PI”## 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.

## Use of foot ratios in Megalithic Astronomy

The ratios of ancient metrology emerged from the Megalithic innovations of count&compare: counting time as length and comparing lengths as the longest sides of right triangles. To compare two lengths in this way, one can take a longer rope length and lay it out (say East-West), starting at the beginning of the shorter rope length, using a stake in the ground to fix those ends together.

The longer rope end is then moved to form an angle to the shorter, on the ground, whilst keeping the longer rope straight. The Right triangle will be formed when the longer rope’s end points exactly to the North of the shorter rope end. But to do that one needs to be able to form a right angle at the shorter rope’s end. The classic proposal (from Robin Heath) is to form the simplest Pythagorean triangle with sides {3 4 5} at the rope’s end. One tool for this could then have been the romantic knotted belt of a Druid, whose 13 equally spaced knots could define 12 equal intervals. Holding the 5th knot, 8th knot and the starting and ending knots together automatically generates that triangle sides{3 4 5}.

Continue reading “Use of foot ratios in Megalithic Astronomy”## A Lecture introducing Sacred Number and the Lords of Time

… given as the John Michell Memorial Lecture for

at Megalithomania 2015 in Glastonbury

- The overhead slides can be found at Academia.org.
- A flyer for the book launched by the lecture, here.
- The publisher’s page for the book is at InnerTraditions.com.

- A flyer for the book launched by the lecture, here.

## Chalk Drums to Symbolise Pi and Layout Monuments

*December 2016 in numbersciences.org Hits: 3872*

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.

Continue reading “Chalk Drums to Symbolise Pi and Layout Monuments”## Thornborough Henge as Moon’s Maximum Standstill

The three henges appear to align to the three notable manifestations to the north west of the northerly moon setting at maximum standstill. The distance between northern and southern henge entrances could count 3400 days, each 5/8th of a foot (7.5 inches), enabling a “there and back again” counting of the 6800 days (18.618 solar years/ 19.618 eclipse years) between lunar maximum standstills.

Continue reading “Thornborough Henge as Moon’s Maximum Standstill”## Number Symbolism at Table des Marchands

Table des Marchands, a dolmen at Lochmariaquer, can explain how the Megalithic came to factorise 945 days as 32 lunar months by looking at the properties of the numbers three, four and five. At that latitude, the solstice angle of the sun on the horizon shone along the 5-side of a 3-4-5 triangle to east and west, seen clearly at the Crucuno Rectangle "Lunar Counting from Crucuno Dolmen to its Rectangle".

Before numbers were individually notated (as with our 3, 4 and 5
rather than |||, |||| and |||||) and given positional notation (like our
decimal seen in 945 and 27), numbers were lengths or marks and, when marks are
compared to accurately measured lengths measured out in inches, feet, yards,
etc. then *each vertical mark would naturally
have represented a single unit of length*. This has not been appreciated
as having been behind marks like the cuneiform for ONE; that it probably meant
“one unit of length”.

## Earth and Moon within Westminster’s Coronation Pavement

Our modern globes are based upon political boundaries and geographical topography yet they have geometrical predecessors, which described the world as an image, diagram or schemata. The original idea for the form of the world was summarised within a simple two dimensional geometry, like an eastern mandala or yantra.

Such a diagram was built into the Cosmati pavement at Westminster Abbey, built by Henry III and dedicated to the Saxon King and Saint Edward the Confessor. This exotic pavement became the focus for the Coronations of subsequent English then British monarchs.

Continue reading “Earth and Moon within Westminster’s Coronation Pavement”## Musical Tones of the Outer Planets

My crucial entré to planetary harmony came when I noticed musical ratios in the synodic time periods of Jupiter and Saturn relative to the lunar year. This approach differs from the norms for “harmonies of the spheres” (a.k.a. Musica Universalis) which are geometrical and spatial, rather than temporally harmonic.

The planetary harmony I found within synodic periods became the subject of my new book *The Harmonic Origins of the World (pub. *2018). These synodic ratios have been parts of my work from c. 2000, then expressed as “matrix diagrams” (*Matrix of Creation, *figure 2 below). In my new book, I show how **ancient tuning theory** seems to have presented the same information, in a different type of matrix (see figure 4).

Below I connect the outer planets using two additional (and useful) kinds of diagram, the right-angled triangle (figure 1) and the Pentad (figure 5), the latter developed in the 20th century within a discipline called *Systematics. *

## The Three Worlds at Gavrinis

*following on from previous post,* *an article by M Guillaume found inAAK 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?

Continue reading “The Three Worlds at Gavrinis”## 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?

Continue reading “Gavrinis: On Crossing the Three Thresholds and Entering The Room”