Ways of Purchasing: This large-format book, richly illustrated in color throughout, can be seen in the sidebar (on mobiles, below the tag cloud) or visit Inner Traditions.
above: Carreg Coetan Arthur portal dolmen in Newport, Pembrokeshire.
The prehistory of sacred geometry was the late stone age, when the stone circles, dolmens, and long alignments to astronomical events on the horizon, used megaliths (large stones) in geometrical ways. Their geometries served their quest to understand the heavens, without telescopes or arithmetic, by using counted time periods as geometrical lines, squares and circles. Geometry, supplemented by the days counted between alignment events, was therefore a prelude to sacred and then secular geometry.
By developing early geometrical methods, they forged an enduring cultural norm lasting millennia, as part (or not) of the more-familiar aspect of the neolithic, innovating an agricultural pastoralism, that could support settlements, cities and, only then, the great civilizations of the middle and far east. It was civilization that generated our earliest written histories; these still powering our historical context and leading the basic notion of economic progress and territorial expansion, as superior to all that went before.
There is a great way to express pi of 22/7 using two concentric circles of diameter 11 and 14 (in any units). Normally, a diameter of 7 gives rise to a circumference of 22, when pi is being approximated as 22/7 (3.142587) rather than being the irrational number 3.141592654 … for then, the 14 diameter should have a circumference of 44, which is also the perimeter of the square which encloses a circle of diameter 11.
The square of side 11 and the circle of diameter 14 will both have the same perimeter.
Figure 1 The Equal Perimeter model of two circles, the smaller of which has an out-square of equal perimeter to the greater circle
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)
Einar Palsson [1, at end] saw that the myths of foundation for Iceland’s settlement in 930 had Pythagorean roots. Since then Petur Halldorsson has identified patterns that could not have been influenced by Pythagoras (c. 600 BC) and Pythagoras was known to have adapted the existing number sciences found (according to his myth) from Egypt to China.
Such patterns, called Cosmic Images by Halldorsson [3], seek to establish a geometric connection between places on the landscape and on the horizon, here in the south-western region near Reykjavik, the only Icelandic city. The spirit of a region or island was integrated through organising space in this way, according to centers (Things) of circles and their radius and diameter as numbers of paces, circles punctuated with places and alignments to other places, horizon events or cardinal directions. John Michell provided a guide to some of the techniques in his books [2, at end].
Figure 1 The Cosmic Image east of Reykjavik proposed by Palsson
In 1972 John Michell inferred an enormous ten-sided form nearly sixty three miles across, in which important historical and neolithic sites had been intended as ten vertices around an ancient centre, signified by a Whiteleafed Oak.
Figure 1 The Decagon of Perpetual Choirs, anchored upon Stonehenge, the Solstice sunrise in summer and set in winter
Michell had previously [1991 now The Sacred Center, 2009] developed the idea of the enchantment of the land as an actual practice; land areas were enchanted by using a geometrical pattern integrated with myths and ritual calendars, enacted within that framework. This was long before, around 930, such a pattern was being established of thing-places in Iceland. The idea of thing places is still find-able in English names such as Goring, the centre northeast of Stonehenge, where the summer solstice sun arose.
“Perpetual choirs were a Celtic institution, from pagan into early Christian times. In Iola Morganwg’s Triads of Britain, translated from Welsh, it is stated that ‘in each of these three choirs there were 24,000 saints; that is, there were a hundred for every hour of the day and the night in rotation, perpetuating the praise and service of God without rest or intermission.’ ” – The Measure of Albion
“Three of the choirs were located at Stonehenge, at Glastonbury, and near Llantwit Major in Wales. Others appear to have been at Goring-on- Thames and at Croft Hill in Leicestershire, a traditional site of ritual, legal, and popular assemblies.” The Dimensions of Paradise
