Category: in Britain

Seven, Eleven and Equal Perimeters

above: image of applications involving sacred geometry based upon pi as 22/7 and a circle of equal perimeter to a square, from a previous post.

The geometrical and other relationships between different numbers are easily found to be useful through simple experiments. The earliest approximations to pi (22/7) was key in the megalithic and later ancient cultures, for making circles of a known diameter and circumference, the foremost using the numbers 7 and 11 doubled twice. A staked rope of length seven will create a circumference of 44, to a high degree of accuracy.

But what is pi? it actually connects two different worlds, of extensive linear measure and of intensive rotational measure. As the radius rope is made larger the circle expands from its center but it remains a whole circle, except that its circumference is made up of more “units” all according to the ratio pi = 22/7, in a good approximation.

But measuring a circumference is fiddly, it is circular! In contrast, it is very much easier to work with squares since their perimeter is four times their side length. And in many cases, one does not really need to measure the perimeter. Because of this, the megalithic looked for and discovered an easier procedure in which one could know the circumference of a circle if one could generate the square that has the same circumference now called the equal perimeter model. This was surprisingly simple to grasp and implement.

First of all, one can lay out a linear length, that divides by 4, lets say 28 which is 4 x 7. The length is made up of four lengths, each of 7 units and, a square of side length 7 will have a perimeter of 28, same as the linear length. The square is really just a rolled-up set of 4 lengths at right angles!

The diameter of a circle with 28 units on its circumference must be larger than its incircle of diameter 7 and, if pi is 22/7 then, the diameter will be exactly 14/11 of the side length. Notice that 14/11 is cancelling the seven and eleven in pi as 22/7.

The equal perimeter rope will be staked in the very center of the square. The side of 7 is then 7 x 14/11 or 98/11 units and this, times 22/7 equals 28 – the perimeter of both the circle, and square side-length 7 units. There is no need to calculate this if one draws a triangle ratio {11 14} from the center of the square. This triangle’s slope angle automatically “calculates” or reproportions the cardinal length (whatever this is) into a suitable rope (or radiant) length.

One often does not need to form the circle to know what its perimeter would be through measurement. Once one knows that every square has a twin circle of the same perimeter, this changes thinking. This is particularly significant when forming a circular model of the sun’s path in the year. If the “saturnian” year 364 days was used, it unusually divides by 28 days, and 13, and 7 days; the seven-day week. The square would have a side length of 13 weeks (91 days) and the radius rope would need to be (13 x 7) x 7/11 which, times 44/7 reconstitutes the circumference of 364 days.

My book Sacred Geometry: Language of the Angels has much to say on equal perimeter modelling, which is found throughout the ancient building traditions that followed on from the megalithic period, using the older techniques of metrological geometry alongside the development of arithmetic methods. Click on the Bookshop logo or Google, and find out more.

How Geometries transformed Time Counts into Circles

Above: example of the geometry that can generate one or more circles,
equal to a linear time count, in the counting units explained below.

It is clear, one so-called “sacred” geometry was in fact a completely pragmatic method in which the fourfold nature of astronomical day and month counts allowed the circularization of counts, once made, and also the transmission of radius ropes able to make metrological metrological circles in other places, without repeating the counting process. This “Equal Perimeter” geometry (see also this tag list) could be applied to any linear time count, through dividing it by pi = 22/7, using the geometry itself. This would lead to a square and a circle, each having a perimeter equal to the linear day count, in whatever units.

And in two previous posts (this one and that one) it was known that orbital cycles tend towards fourfold-ness. We now know this is because orbits are dynamic systems where potential and kinetic energy are cycled by deform the orbit from circular into an ellipse. Once an orbit is elliptical, the distance from the gravitational centre will express potential energy and the orbital speed of say, the Moon, will express the kinetic energy but the total amount of each energy combined will remain constant, unless disturbed from outside.

In the megalithic, the primary example of a fourfold geometry governs the duration of the lunar year and solar year, as found at Le Manio Quadrilateral survey (2010) and predicted (1998) by Robin Heath in his Lunation Triangle with base equal to 12 lunar months and the third side one quarter of that. Three divides into 12 to give 4 equal unit-squares and the triangle can then be seen as doubled within a four-square rectangle, as two contraflow triangles where the hypotenuse now a diagonal of the rectangle.

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The Stonehenge Trilithons (Part 2): Day-Inch Counting

In the previous article, it was shown that the form of the trilithons, of five taller double sarsens approximating to a five-pointed star, matches the astronomical phenomena of the successive morning and evening stars, as Venus approaches Earth from the east and then recedes to the west as the morning pass. On approach, the planet rises in the evening sky and then dives into the evening sun and if one traces this motion it have the appearance of a horn. Venus shoots past the sun and reappears in the morning sky as the sun rises, creating another traced horn shape, symmetrical to the evening.

Figure 1

In support of the form of the trilithons resembling five successive double horns of Venus over 8 years, the width of the inner faces can also be interpreted as to their length being one megalithic rod, that is 2.5 megalithic yards. The distance between each pillar is ¼ of a megalithic rod so that, each inner face is divided by 4 of these units which units are 5/8ths of a megalithic yard, the ratio of the practical year of 365 days relative to the Venus synod of 584 days (365 / 584 = 5/8), the common factor between the two periods being 73 days.

The combined inner width of each pair of supports would therefore symbolize 8 x 73 days, or 584 days. Five of these pairs would then be 5 x 584 days, which equals 2920 days, this time period also being 8 x 365 days or eight practical years.

The inner surfaces lie on an ellipse which can be framed by a 5 by 8 rectangle whose sides are exactly the diameters required to form a day-counting circle for 365 day-inches (116.136 inches) and 584 day-inches (185.818 inches). The 365 day-inch circle (shown red and dashed in figure 4) has its centre in the center of the ellipse and so would have touched the two trilithons at A and B, at a tangent to their faces.

Figure 2 The Venus count of 584 day-inches (shown blue and dashed) was concentric to both the bluestone and sarsen circles, sitting inside of the bluestone circle.

The high degree of correlation between,

  1. the five-fold form of the Venus synod and the five couplets of trilithons,
  2. the summed inner widths of the trilithons as being 5 x 8 = 40 units of 73 days = 2920 days.
  3. the out-rectangle of the inner ellipse being 8 by 5 and
  4. the rectangle’s sides being the diameters of two circles of 584 inches and 365 inches, suitable for day-inch counting,

……. points to the 5-fold horseshoe of trilithons as a “temple” to the unique astronomical behavior of Venus in its synodic relationship to the solar year of 365 whole days.

No other compelling explanation exists, though many interpretions have been proposed such as

The Stonehenge trilithons as synods of Venus

Figure 1 The five Trilithons of Stonehenge 3, highlighted in yellow within the Sarsen ring to express the five evening and morning star couplets which occur in eight practical years of 365 days. Plan from Megalithic Remains in Britain and Brittany, Oxford U.P. Central portion is fig.3, upside down to match the horseshoe of trilithons..

Inside the Sarsen ring of Stonehenge, there once stood a group of five trilithons, each made up of two uprights and a lintel stone, repeating the unique style of building found in the Sarsen ring. However the Trilithons were higher than the sarsens, punctuating an elliptical cup shape towards the midsummer sunrise, the axis of Stonehenge and its solstice-marking “heel” stone.

The Horns of Venus

The symbolism therefore involved (a) the Sun, (b) the number five of the trilithons while (c) expressed something involving close pairs. The dominant astronomical significance of the number 5 comes through the brightest planetary phenomenon of all, in which the planet Venus approaches the Earth, as Venus approaches from the east, preceding the Sun in the evening sky. It is often therefore called the Evening Star. Venus then shoots past the sun and reappears in the morning sky, again growing in brightness as the Morning Star.

Figure 2 The Horns of Venus when the evening and morning “stars” are visualised over an extended present moment of the Venus synodic period of 1.6 (⅝) practical years of 365 days. Fig. 2.2 of my Matrix of Creation, Inner Traditions, 2004 . (Drawn by Robin Heath.)

The original astronomers of the megalithic only saw the planetary system from the Earth and not (conceptually) from the Sun, as we do today. That is, they were naturally geocentric whilst the present worldview is heliocentric.

The astronomers could study cosmic time periods without arithmetic, through counting days, using a constant unit length to mark each single day adding up to a fixed length of days. Through such counting they would see 365 whole days between the solstices and (more reliably) between the equinoxes (when the Sun moves most rapidly on the horizon). It was also quite obvious that the horns of Venus were bracketing the Sun, just as the elliptical cup of the trilithons they erected at Stonehenge bracketed the solstitial sun, a sun which travels every day from east to west.

Five-ness in the Zodiac

If the earth was their viewpoint then the Zodiac of the sun’s path over the year could, like the Sarsen Circle, be seen as a circle of 365 days, and when the time between evening or morning stars was counted, the result was 584 days between the horn-like and brilliant manifestations of Venus. 584 days is 219 days more than 365 days. The sun has therefore moved 3/5th of a year forward and hence it became noticeable, as stated above, that 1/5th of the practical year is 73 days, the practical year 5 units of 73 days long whilst the Venus synod is 8 units of 73 days long. The Venus synod therefore has exactly 1.6 (8/5) practical years between its phenomena.

Figure 3 The Horns of evening (E) and morning (M) stars shown upon the circle of the Zodiac, each successive pair 3/5ths advanced within the solar year. [from Joachim Schultz, Movement and Rhythms of the Stars, Floris, 1986, fig 88]

The form of Venus upon the Zodiac therefore describes a 5-fold pentacle star. This would later make the number 5 and all of its properties, sacred by association to the planet Venus who became the leading goddess of the Ancient Near East. The Golden Proportion or Mean (1.618034…), often seen in Classical and Neoclassical architecture, has the number 5 as its root. Also, many living bodies share forms derived from the number 5, or of the Fibonacci approximations to the Golden Mean.

The Fibonacci series (of 1, 1, 2, 3 ,5 ,8 ,13 ,21, …) has successive numbers that sum to give the next number, and each new ratio, between successive numbers in the series, yields an ever-better approximation to the Golden Mean: (2, 1.5, 1.6, 1.6, 1.617, …).

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Sacred Number and the Lords of Time

Back Cover

ANCIENT MYSTERIES

“Heath has done a superb job of collating his own work on the subject of megaliths with the objective views of many other researchers in the field. I therefore do not merely recommend reading this book but can state unequivocally it is a must read.”
–John Neal, British metrologist and researcher and author of Measuring the Megaliths and The Structure of Metrology

“In Sacred Number and the Lords of Time we have an important explanation of how megalithic science was developed. This book is a long-overdue wakeup call to a modern culture that has abandoned this fully developed and astonishingly rich prehistoric model of the physical world. The truth is now out.”
–Robin Heath, coauthor of The Lost Science of Measuring the Earth and author of Sun, Moon and Earth

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Durrington Walls and its massive circle of Pits

Recent analysis of animal bones within Durrington Walls indicated, to the archaeologists involved, that people had travelled there from all over the British mainland, along with animals then eaten inside the henge[1]. But what would these people be doing there? It had earlier been suggested that an elite responsible for building Stonehenge lived in a wooden roundhouse within the henge ([2] see figure 1). So, people may have come from elsewhere to help the building works now found between Stonehenge and Avebury.

Figure 1 Reconstruction of the likely roundhouses within the Durrington henge, based on post-hole evidence [2]

More recently, pits have been found [3] within a circular strip that I notice lies between 3168 feet and 4038 feet from Durrington Walls, a boundary 864 feet wide. The pits may contain the material remains of the building elite and perhaps of those workers who died, functioning like nearby barrows but vertically.

This post aims to explain why this might have been done according to a significant geometrical pattern. In the megalithic, numbers played an active role and this perhaps inspired the myth of Atlantis recorded by Plato – the classical Greek writer who transmitted the ancient notion that numbers had a causative role in forming the “world soul”, rather than our usage for number: a means to quantify things within civilized societies or laws of nature.

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