Geometry 6: the Geometrical AMY

By 2016 it was already obvious that the lunar month (in days) and the PMY, AMY and yard (in inches) had peculiar relationships involving the ratio 32/29, shown above. This can now be explained as a manifestation of day-inch counting and the unusual numerical properties of the solar and lunar year, when seen using day-inch counting.

It is hard to imagine that the English foot arose from any other process than day-inch counting; to resolve the excess of the solar year over the lunar year, in three years – the near-anniversary of sun and moon. This created the Proto Megalithic Yard (PMY) of 32.625 day-inches as the difference.

Figure 1 The three solar year count’s geometrical demonstration of the excess in length of 3 solar years over 3 lunar years as the 32.625 day-inch PMY.

A strange property of N:N+1 right triangles can then transform this PMY into the English foot, when counting over a single lunar and solar year using the PMY to count months.

The metrological explanation

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Astronomy 2: The Chariot with One Wheel


What really happens when Earth turns? The rotation of Earth describes periods that are measured in days. The solar year is 365.242 days long, the lunation period 29.53 days long, and so forth.

Extracted from Matrix of Creation, page 42.

Earth orbits the Sun and, from Earth, the Sun appears to move through the stars. But the stars are lost in the brightness of the daytime skies and this obscures the Sun’s progress from human view. However, through observation of the inexorable seasonal changes in the positions of the constellations, the Sun’s motion can be determined.

The sidereal day is defined by the rotation of Earth relative to the stars. But this is different from what we commonly call a day, the full title of which is a tropical day. Our day includes extra time for Earth to catch up with the Sun before another sunrise. Our clocks are synchronized to this tropical day of twenty-four hours (1,440 minutes).

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Astronomy 1: Knowing North and the Circumpolar Sky

about how the cardinal directions of north, south, east and west were determined, from Sacred Number and the Lords of Time, chapter 4, pages 84-86.

Away from the tropics there is always a circle of the sky whose circumpolar stars never set and that can be used for observational astronomy. As latitude increases the pole gets higher in the north and the disk of the circumpolar region, set at the angular height of the pole, ascends so as to dominate the northern sky at night.

Northern circumpolar stars appearing to revolve around the north celestial pole. Note that Polaris, the bright star near the center, remains almost stationary in the sky. The north pole star is constantly above the horizon throughout the year, viewed from the Northern Hemisphere. (The graphic shows how the apparent positions of the stars move over a 24-hour period, but in practice, they are invisible in daylight, in which sunlight outshines them.)
[courtesy Wikipedia on “circumpolar star”, animation by user:Mjchael CC-ASA2.5]

Therefore, the angular height of the pole at any latitude is the same angle we use to define that latitude, and this equals the half angle between the outer circumpolar stars and the pole itself. For example, Carnac has a latitude of 47.5 degrees north so that the pole will be raised by 47.5 degrees above a flat horizon, while the circumpolar region will then be 95 degrees in angular extent.

It is perhaps no accident that the pole is called a pole since to visualize the polar axis one can imagine a physical pole with a star on top, like a toy angel’s wand. The circumpolar region is “suspended” around the pole like a plate “held up” by the pole. Therefore, a physical pole, set into the ground, can be used to view the north pole from a suitable distance south (i.e., with the pole’s top as a foresight for the observer’s backsight). Such an observing pole would probably have been set at the center of a circle drawn on the ground, representing the circumpolar region around the north pole. This arrangement, a gnomon,* existed throughout history but usually presented as part of a sun dial.

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The Discovery of a Soli-Lunar Calendar Device at Le Manio

by Robin Heath

In 2009 I returned to Plouharnel, again for the Solstice Festival, and undertook my own research both before and after the four day event. Howard Crowhurst had undertaken a great deal of theodolite and tape work at a well known site called Le Manio. This collection of surviving monuments forms an exceptionally rich group of astronomical alignments which together carry enormous ritual significance in that these sites hold information about human conception, the gestation period and ritual use of geometry and metrology. Howard understands the site to the point where his three hour workshop covered much of this material, and the implications of it were clearly understood by non-specialists. Those readers who have the chance to attend the Festival, and who speak either English or French, should regard this experience as a megalithic ‘must’. Howard is an exceptionally good communicator of what are often seen as difficult areas of megalithic research, and he is astonishingly good at passing these ideas on to his audience with a great deal of clarity, enthusiasm and humour.
It was during Howard’s seminar/workshop that he invited me to set up his theodolite within the Le Manio Quadrilateral, a curious site near the 6.5 metre high ‘Giant of Le Manio’. This done, I noticed something I had been searching for for twenty years. Read on…!

Le Site Mégalithique du Manio à Carnac

by Howard Crowhurst

Perched on a hill in the forest north of the Carnac alignments, a megalithic site has escaped the fences that have littered the landscapes of the region for several years. These are the menhir and the quadrilateral of Manio. From the outset, the large menhir impresses with its dimensions. Nearly 5m50 high, it is the highest standing stone in the town.

More discreet, the quadrilateral caps the top. 90 upright and contiguous stones, varying in height between 10 cm and 1m60, make up an enclosure approximately 36 meters long and 8 meters wide on average, because the long sides converge. The stones at the ends draw a curve. Four stones to the northeast form the remains of a circle. Two menhirs, much larger than all the other stones in the quadrilateral, open a kind of door in the south file. This particular form questions us. What could she be used for? Was it a meeting place, maybe an enclosure for sheep? In fact, what we see today is probably only the outer skeleton of a larger monument, a mound of stone and earth that contained a chamber inside. Other remains complicate the whole, unless they help us solve our puzzle. Hidden in the brambles and brush, we can discover a stone on the ground of rounded shape. These curves are reminiscent of the belly of a pregnant woman. She is nicknamed the “Lady” of the Manio.

Day-inch counting at the Manio Quadrilateral

It is 10 years since my brother and I surveyed this remarkable monument which demonstrates what megalithic astronomy was capable of around 4000 BC, near Carnac. The Quadrilateral is the earliest clear demonstration of day-inch counting of the solar year, and lunar year of 12 lunar months, both over three years. The lunar count was 1063.125 day-inches long and the solar 1095.75 day-inches, leaving a difference of 32.625 day-inches. This length was probably the origin of a number of later megalithic yards, which had different uses.

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