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THE STONEHENGE CODES - New Light on Ancient Knowledge

by Professor David P Gregg (retired)


Hello there and welcome to my analysis of Stonehenge…and the rest. No doubt you are wondering how I came to take it on… so am I. Some of it may have to do with my professional background and a life long interest in several fields that seem to collide at Stonehenge. 

Let me start at the beginning. I was born in Liverpool between VE day and the dropping of the first atomic bomb on Hiroshima. My now advanced age and early retirement have provided the time to consider the megalith problem. I was educated at West Derby Technical High School in Liverpool before going on to the university. Later I joined Unilever Research in Wirral as a chemical engineer. Noting my profound ignorance my superiors provided a scholarship to Lancaster University to read for a second degree in Systems Engineering. This discipline , a close cousin to Operational Research, combining all kinds of topics from mathematical modelling and statistics to economics had been made highly fashionable by the success of NASA’s space programmes which relied heavily on ‘SE’.

Back at Unilever boredom was kept at bay by applying modelling and optimisation techniques to everything from consumer behaviour, plant control , factory scheduling and design to the strategic re-design of continental scale supply chain systems. Along the way I had the privilege of managing research groups in systems engineering, statistics and artificial intelligence and some very talented people in Unilever and in British, US and European academia. Dealing with EU funding bureaucracy deserves a book on it’s own. Along the way , for fifteen years, I was also a visiting professor at a leading UK university. Along the way for some years I had the exciting privilege to work with the Santa Fe Institute in New Mexico on applications of Complex Systems Theory to business and to advise the Unilever Research Director on this and other novel, emerging technologies.

In New Mexico I got to learn something of the Anazasi civilisation and their descendants , of their remarkable towns and their astronomy which rang bells in relation to British megalithic sites and my readings on other ancient societies. It set me thinking. (I should record that I have been an astronomer of sorts since the age of eleven. My current telescope is an excellent 12 inch Dobsonian reflector used primarily on the Moon and planets). My amateur studies of conventional history and pre-history set against the apparent architectural and other achievements of these peoples increasingly jarred. Add to that hints from the mythologies of several cultures and I began to wonder. Could it be that our current ‘knowledge’ models of ancient pre-literate and even literate societies are wrong? Stonehenge with it’s many features and long pre-history of cultural significance seemed a good place to start exploring the question. If there was ‘nothing there’ on the ground fairly simple geometric and mathematical analysis should quickly prove it. Well it appears that there is ‘something there’ but quite what it is is equally difficult to decide never mind prove. I leave that to the future and to comparative studies of other sites like Avebury, Woodhenge and Newgrange now under way. 

Other Interesting Stories


Enjoy this report with an open but critical mind. It is still a work in progress. It is also an exercise in raising new questions about Stonehenge and possibly about providing a few tentative answers. The reader can judge. Hopefully a few with the relevant backgrounds will be encouraged to take a closer look at my suggestions.

Stonehenge has variously been defined as a work of the Devil ; as a communal ritual centre for several, successive local cultures; as an exercise in sophisticated architectural geometry; as a calendrical device or even an astronomical observatory dedicated to the cycles of the Sun and Moon and to such arcane phenomena as eclipses and their prediction. Over several centuries now the various theories have risen and fallen in popularity , sometimes as evidence has improved, but more often on the basis of ‘fashion’. 

This report began with a modest aim : to rigorously test the proposition , raised from time to time, that Stonehenge features, built across a millennium and more, are dimensionally related via formal geometry or other scaling principles. The idea of such ‘design continuity’ is of course anathema to conventional archaeological beliefs. But just suppose it is true. It would have profound implications about the successive cultures who occupied the area and the transmission of ‘technical’ knowledge between allegedly pre-literate peoples. 

Given the author’s professional background in engineering, system’s analysis and astronomy the task turned out to be fairly simple in a technical sense but nearly impossible to complete. (note : no computers were harmed in this study. Standard drawing instruments and a £20 pound engineering calculator sufficed). Clear dimensional relationships between many features were found but these only raised further questions and uncovered remarkable coincidences also demanding investigation. The report examines these in detail and the reader can decide whether or not he or she believes these ‘outrageous’ coincidental results. Here is a brief summary of some of my findings. 

1. All the structures of Stonehenge , irrespective of supposed date in the building sequence, are dimensionally related via the geometry of regular polygons inscribed in the Aubrey Circle. The geometries of the heptagon, pentagon and square are prominent. E.g. A heptagon construction probably underlay the 56 hole Aubrey Circle and that construction also defines the much later Sarsen Circle and the even later Z and Y rings. The proposed heptagon construction also accurately encodes the site latitude. 

2. Several times feature dimensions measured in Professor Thom’s megalithic yards correspond to well known lunar periods. Frequently dimensional ratios correspond accurately to ratios of lunar / solar cycles and in the Z and Y ‘spirals’ to the proportions of the lunar orbital ellipse. This was totally unexpected. 

3. Often, because of pentagon and heptagon properties, dimensional ratios between features involve simple functions of phi, the golden section. Curiously these phi functions often match the ratios of key astronomical cycles. Did the builders recognise and deliberately exploit these coincidences in their designs?

4. It is accepted that the bluestone horseshoe of 19 stones may record the 19 solar years of the Metonic cycle or the 19 eclipse years of the Saros cycle. Similarly the 30 holes of the Y ring and the 29 holes of the Z ring could provide the basis of a lunar calendar of alternative 29 and 30 day ‘months’ , an ancient calendar still used in some modern cultures. It was also found that the QR complex could support the simple tracking of several cycles including the Metonic and longer, more accurate, Callippic. Several features could also support the simple tracking of the synodic and sidereal periods of the bright planets such as Venus, Jupiter and Saturn via stone counts. The author also finds intriguing parallels between Stonehenge stone counts and the remarkable Antikythera astronomical ‘computer’ of the 2nd century B.C. with its dozens of bronze gears. Where that device used rotating gears, at Stonehenge, similar cycle tracking results may have been achieved using fixed stones and rotating ‘priests’. 

5 Re-examination of the use of the 56 Aubrey holes gives new support to Professor Hoyle’s proposed mechanism for eclipse prediction and identifies other cycle tracking duties. The association of a polygon of 56 sides with Typhon / Seth in Egyptian myth who, according to Plutarch, is also explicitly identified with the shadow of the Earth covering the Moon in lunar eclipses is also examined along with other helpful numerical traditions and myths. The use of numerical puns in the myths of literate societies like Egypt and Greece hint at similar practices among the ‘non-literate’ megalith builders…but written in stone. 

6 The intriguing results on Thom’s megalithic yard at Stonehenge encouraged the author to look wider at ancient metrics with disturbing results. A unit identical to Thom’s appears more broadly than in megalithic Europe and over a vast sweep of time. It is certainly related to other ancient metrics and in simple ways. The possible origins and reconciliation of these metrics are discussed in appendices along with several other ‘anomalous’ and surprising findings. Those of a nervous disposition should avoid them.

The reader is free to draw his or her own conclusions on all this strange material but the author concludes that there was not one motivation for building at Stonehenge over the centuries, but several. The builder’s no doubt had motives as complex as any builders of great monuments : a mixture of serving God and Mammon while projecting the power of the rulers and celebrating their own special skills and elite knowledge, which may have provided practical benefits to the state including impressing and controlling the population. How did it all begin? Most probably with a practical interest in defining a calendar via easily observed astronomical cycles. This in itself leads us into simple geometry and calculation. Over time more subtle phenomena were recognised and at some point coincidental links between the geometry of triangles and polygons on Earth and the cycles of heaven became clear. Did that trigger the Stonehenge phenomenon or was this merely the culmination of knowledge won elsewhere over many centuries? Seeing such links the builders cannot fail to have been moved by a sense of wonder and perhaps to worship, ceremonial and ritual. There is probably not one Stonehenge Code but several, intricately interwoven and as rich and complex as the human mind itself. Perhaps one day, with open minds and a rejection of narrow reductionism, we will see as they saw when the world was new. 

Copyright 2010 by Professor D P Gregg (retired)
All Rights Reserved. Presented with permission of the author.

Official Website: www.stonehenge-codes.org 


Copyright ©  2010 by D P Gregg


  1. Introduction 3

  2. Phase I : Ditch, Banks & Aubrey Circle. 8

  3. Phase III a-c / i : Heel Stones. Avenue, Station Stones & QR complex. 25

  4. Phase III ii : Sarsen Circle & Trilithons 54

  5. Phase III iv-vi : Bluestone Oval, Trilithon Bluestone Circle, YZ holes. 60

  6. Geometry & Feature Dimensions 87

  7. Dimensional Continuity and Phi 94

  8. Stone Dimensions 98

  9. Phi and Astronomical parameters in Ancient Architecture 100

  10. Probability and Coincidence 116

  11. Conclusions 121


  1. Constructing The Aubrey Circle Using A Heptagon
    1A The Method 146
    1B Exact Heptagon Parameters 149
    1C Deriving the Sarsen Circle From The Aubrey Circle. 150

  2. A Curious Property of The Y and Z Circle Dimensions 151

  3. The Station Stone Rectangle and The Aubrey Pentagon 154

  4. Greece, Egypt and Older Friends 154

  5. Ancient Metrics and The World Egg 173

  6. Eclipse Prediction at Stonehenge 212

  7. Astronomical Cycles and Pythagorean Musical Theory. 224

  8. Formal Construction Of A Pentagon 228

  9. Statistical Evidence for The Megalithic yard. 231

  10. A Simple Method For Measuring Lunar Diameter 234

  11. Other Planetary Correlations 239

References 243


In contemplation if a man begins with certainties he shall end in doubts; but if he is content to begin with doubts , he shall end in certainties.   

-- Francis Bacon 

1. Introduction 

This report began as a simple re-examination of the design features of Stonehenge beginning seriously in 2002. It is a book of questions and perhaps, the reader will eventually decide, a few answers. The author wondered whether any relationships existed between Stonehenge features and whether such relationships could help confirm or reject the many claims of links to astronomical phenomena, namely the cycles and movements of the Moon, Earth and Sun. Such links were indeed found, and in unexpected ways, but these links merely raised yet more and deeper questions about the scientific and mathematical knowledge of ancient societies. These provocative questions have been explored in a series of extensive appendices while the body of the report attempts to restrict discussion to the original task of understanding Stonehenge design. That in itself has many surprises. Either we have coincidences of .astronomical. or indeed .monumental. improbability linking monument features to the geometries of regular polygons and Pythagorean triangles , the Golden Section, phi and numerous lunar/solar/terran parameters and cycles, or something is very wrong with our assumptions about the knowledge and sophistication of the megalith builders. However these disturbing observations may be merely the tip of the iceberg. The appendices contain broader material which those of a nervous disposition should avoid. Read them and you may never see the history of technology or indeed of human intellectual development in the same way again. 

Stonehenge has received more attention from would be analysts than any other ancient monument with the possible exception of the Great Pyramid. Archaeologists have seen it as a great communal ritual centre serving the several cultures who successively occupied it.s environs and buried their dead on the surrounding plain. The astronomers also came, measured, and computed and saw sophisticated representations of the movements of the sun and moon and perhaps, even, mechanisms for the prediction of eclipses. The geometers came 4 and pointed to the precision with which many of the features of the monument are laid out and noted, in a few instances, that certain features seem to be geometrically related in shape or dimension. We will see that these facets of interpretation are not mutually exclusive if we examine all the facts and decline to define human beings through the lenses of particular narrow, 'disciplines'. The reality, still only dimly glimpsed in this report, is possibly much, much richer and humane.

Much work has been done but still the argument has ebbed and flowed between those who deny the 'builders' anything more than an ability to chip stone and organise work gangs , and those who see evidence of considerable knowledge of geometry, geodesy and astronomy and of a practical capability to express that knowledge on the landscape. 
Archaeologists have repeatedly argued that a pre-literate agrarian society could not have achieved those things the 'scientists' claimed. Above all they reject the notion of continuity : that monument features separated by centuries could be related.  Secondly , that few of the so-called astronomical alignments observed in the monument complex are accurate enough to confirm the proposed solar-lunar hypotheses.  Thirdly that without observational continuity on scales of centuries such alignments could not be discovered anyway (1,15). 

These reasonable objections are challenged by three simple facts : 

  • the station stone rectangle (Figure 4) is within a few miles of that unique latitude at which summer solstice sunrise and lunar standstill azimuths are at right angles to each other ; 

  • the Sarsen circle diameter is clearly determined by the heptagonal construction 'scaffolding' of the Aubrey circle yet these features are separated in time by several centuries ; 

  • the heptagonal Aubrey circle construction also simply encodes the site latitude to within a mile of the correct value. As a check a similar result is found for the earlier Avebury site. 

These isolated, awkward coincidences are sometimes accepted as intriguing but apparently do not compel the opening of closed minds. 

Consequently the author has re-examined the dimensions of all key features of the monument across some 1,400 years of development and sought out other, systematic correlations. Dimensions were collected from several reputable sources including Professor Thom.s work and checked by personal measurement on published scale plans where possible. More recently 'Hengeworld' (35) was particularly useful as a compendium of recent data and archeological 5 interpretation on Stonehenge and other major sites based on the English Heritage collection , .Stonehenge In It.s Landscape. ( 40), although this author differs from it in many points of interpretation. Most recently .Solving Stonehenge. has demonstrated clearly the central role of geometry at Stonehenge and what can be achieved in practical monument layout (38 ). Some measurement uncertainties are inevitable, for example where only stone holes remain, but in practice distances can be estimated to within a few feet.(Please note that no computer was harmed in making these analyses : everything was done by careful observation aided by a modest drawing board , standard drawing instruments and a £G20 engineering calculator).

The key principle in this analysis is to let the stones speak for themselves : to estimate dimensions as closely as possible and then to look for patterns. No patterns have been rejected on the basis that they could not exist because of currently held archeological timescales or a priori beliefs about the ability of the designers. Even the relative timescales of major features remain very uncertain (35). Where there are uncertainties in dimensions and stone counts alternative interpretations have been explored. The totality of the raw pattern data should be judged as a whole. It was found that all .circles., the trilithon horseshoe, the bluestone oval and the station stone rectangle are dimensionally related, through simple geometry, to the .original. Aubrey circle design. The probability of this occurring by chance is shown to be very small. Remarkably and indisputably the scaling between features is repeatedly and simply related to phi and sometimes pi. The reason for this is not mysterious but lies in the properties of heptagons, pentagons, octagons and triangles which appear to define the design. This is demonstrated by construction and , for certainty, trigonometrical calculation. Using phi and pi functions provides a convenient way of highlighting numerical regularities within and between monument features and emphasises commonalities of design but geometry, not advanced mathematics, was king. Some of these numerical functions are obvious and perhaps intentional, others less so and perhaps consequential to primary geometrical design choices. 

It also turns out that by coincidence phi is very closely connected numerically with various lunar/solar/terran parameters and cycles recognized by other early cultures which may understandably have captured the attention of the designers : the heavens above and human geometry below display the same numbers ! Did the designers know? Did it inspire their 6 designs? Does this explain the widespread appearance of the same proportions in megalithic monuments? The reader can judge for himself. This possible link has been explored in the appendices by reviewing phi in other megalithic constructions in Europe and elsewhere. Repeatedly we find evidence for .interest. in the same limited set of Pythagorean triangles and polygons which turn out, by coincidence, to be related to key lunar parameters. This coincidence appears to have been shared by and possibly to have inspired several ancient cultures including classical Greece. 

The author has also sought independent evidence, other than alignments, for the dedication of Stonehenge to recording solar-lunar movements. It transpires that the QR and YZ circle pairs both repeatedly encode accurate information on lunar orbital dynamics.The encoding scheme is different in each case , those for the later YZ pair being direct, elegant and repeated to ensure we get the message. Moreover some of the YZ features defining these lunar parameters are set out in prime, integer multiples of Professor Thom.s much maligned .megalithic yard. . Conversely the R and QRmean circle diameters of Stonehenge II have non-integer diameters in megalithic yards apparently directly recording the draconic and synodic months. These numbers also occour as stone counts in Stonehenge. Even in the earliest phase the bank dimensions closely record lunar cycle information and this turns up again in the latest features 1400 years later. As we move through the construction phases coincidence mounts upon coincidence until chance is difficult to accept as an explanation. Let the reader judge. 

Was the interest of the builders .scientific. in the narrow , modern sense , a proposal which seems to disturb some archeologists? Frankly this has no bearing on whether they did or did not encode astronomical knowledge in the monument. However the author points out that as recently as Isaac Newton we have a polymath who not only explained the mathematics of planetary motion and gravity, and revolutionised our knowledge of optics but also studied alchemy and spent decades in arcane studies of the Bible and the Book of Revelation. Johannes Kepler , father of planetary dynamics, cast horoscopes for a living. If the author is allowed an opinion, for most of our history humans were not simply divisible into Snow.s two caricatured .cultures. and in reality this is still true. Our Stonehenge builders over the centuries no doubt had motives as complex as any builders of great monuments : a mixture of  serving God and Mammon while projecting the power of the rulers and celebrating their own special knowledge and elite skills, which occasionally may have had practical uses for the state including impressing and controlling the population. Nevertheless seeing the remarkable coincidences between earthly geometry and heavenly dynamics they cannot fail to have been moved by a sense of wonder and perhaps to worship, ceremonial and ritual. There is not one Stonehenge code but several, intricately interwoven and as rich and complex as the human mind itself.

The author has also looked again at Thom.s data for hundreds of true circles and it clearly demonstrates, via basic statistical principles, that a standard metric, not pacing was used to scale, and combined with geometry, layout megalithic monuments. The evidence strongly supports the existence of this metric. These results were so intriguing that the megalithic yard hypothesis was further explored in the appendices with surprising results. The megalithic yard was found independently in artifacts associated with Stonehenge and other parts of Britain. Several well established metrics from across Eurasia, spanning five millennia, were found to be closely and simply related. The deep cultural and historical implications of these disturbing relationships are briefly explored. 

Professor Hoyle.s hypothesis that the 56 Aubrey holes were used as an eclipse predictor is explored and extended. The 56 hole circle is very well suited numerically to tracking the Metonic, Saros and other eclipse cycles and lunar apsides cycle as well as the shorter solar-lunar periods. It brings out and exploits subtle relationships between the cycles which would make long term calibration of the prediction system failsafe. Hoyle was very probably right. It is also highly likely that other features were used to record and count astronomical cycles, sometimes directly and sometimes in combination. Cycle counting explains otherwise inexplicable stone numbers in several features. Unexpectedly it turned out that the sidereal and synodic periods of the bright planets, in particular Venus and Jupiter are also easily recovered from simple stone counting in Stonehenge features. 

The geometrical and astronomical knowledge displayed in Stonehenge and elsewhere is disturbing to the accepted model of the history of .science.. It raises the question of whether 8 ancient .technical. knowledge has been badly underestimated in general. This is explored in the appendices by looking at new evidence such as the Antikythera analogue astronomical computer which demonstrates remarkable theoretical and practical sophistication in a device built in the 2nd century B.C. It uses dozens of bronze gears, some with prime numbers of teeth in ratios also used at Stonehenge in stone counts and circle dimensions. The same thinking and logic arguably underlies both devices to achieve the same ends. The appendix also looks briefly at the Nabta culture of 6000 - 4000 B.C. A stone circle therein turns out to be constructed using familiar Pythagorean triangles involving phi which accurately reflect the latitude of the site. The construction is similar to that of British megalithic .Type 2 eggs.. The circle axis is also astronomically orientated. We will also look at the origins and relationships of various distance metrics in human dimensions, at the .sacred. geometry we find in the megaliths and other monuments and, just possibly, at ancient .scientific. methods of metrical scaling. Considering all this material in addition to the Stonehenge evidence the author tentatively concludes that our implied historical models of intellectual development are simply wrong.

The book is available here: www.stonehenge-codes.org 




The book is available here: www.stonehenge-codes.org 

Stonehenge Revealed
David Souden

The latest archaeological methods provide fascinating insights into the perplexing history of Stonehenge. Over 200 striking full-color photographs reveal the collection of stones from various perspectives, allowing readers to sense the mysterious aura that surrounds this place. Maps and charts.

Stonehenge Complete 
Christopher Chippindale

The book is richly illustrated throughout with photographs going back over 100 years, plus drawings and paintings that date back at least to the 16th century. 
In this book you get to meet many interesting characters who left their mark on Stonehenge and its interpretation, from John Aubrey, William Cunnington, Inigo Jones, Colin Renfrew to modern new age researchers. They and their concepts are all presented here.
This book is a start for anyone interested in learning more about Stonehenge. It is written with a sense of humor, and in a very readable style. You can then branch out to read more in-depth studies of the various theories and paradigms that you are interested in. 

Great Stone Circles : Fables, Fictions, Facts
Aubrey Burl

For those who are enthralled by Stonehenge and the many other awe-inspiring prehistoric stone circles of Britain, archaeologist Aubrey Burl now offers fascinating insights into their many mysteries. In this book he selects a dozen of the most evocative rings and proposes sometimes surprising answers to questions about the circles-their purpose, construction, age, design, art, legends, and relation to astronomy.

A Guide to the Stone Circles of Britain, Ireland and Brittany (1995)
Aubrey Burl  

This practical and knowledgeable guidebook is the first to deal comprehensively with the stone circles of Britain and Ireland and with the cromlechs and megalithic "horseshoes" of Brittany. Filled with fascinating information, useful maps, and arresting photographs, this invaluable resource describes over 400 sites and discusses the archaeology and architectural features of each ring.

Great Architecture of the World
by John Julius Norwich (Editor), Nikolaus Norwich, Nikolaus Pevsner


CIVILIZATION ONE: Uncovering the Superscience of Prehistory

by Christopher Knight and Alan Butler

The Stonehenge Observatory.com
Dean Talboys, 2008

Great Architecture of the World
John Julius Norwich, editor. 

London: Mitchell Beazley Publishers, 1975. photo, p26.  An accessible, inspiring and informative overview of world architecture, with lots of full-color cutaway drawings, and clear explanations. 

Book Description
A unique and sumptuously produced overview of architecture through the ages, with extraordinary one-of-a-kind cutaway drawings. Here is a brilliantly accessible chronicle of the greatest monuments created by mankind, told by fourteen of the most distinguished architectural historians and beautifully illustrated with more than 800 original diagrams, annotated drawings, and photographs-both a browser's delight and a superb reference tool.

Stonehenge: A New Interpretation of Prehistoric Man and the Cosmos
John David North

In a book that finally solves the riddle of Stonehenge, scholar John North draws on more than 15 years of research to offer a masterful "case-closed" study in which he examines the monument from all available angles --archeological, astronomical, and spiritual --and considers relevant research from other prehistoric remains in Britain and Northern Europe. 

The Sacred Earth
Courtney Milne

Kailasa Temple, cave #16 at Ellora, India 

These two stunning collections of photographs should carry a warning: incurable wanderlust may result from examining either one. Although different in format ( The Sacred Earth is in color, while Planet Peru is black and white) and subject matter (Milne traveled the Earth to photograph places he feels to be special, whereas Bridges concentrates solely on aerial photos of Peru), both author/photographers present a sweeping panoply of landscapes that, through the ages, have instilled wonder in the beholder. The authors have a deep sense of appreciation and responsibility for the natural splendors of the Earth; both use the word sacred in its broadest sense, meaning the feeling of transcendence experienced by those fortunate enough to have shared the same vistas. Bridges's book is a vertical exploration of Peru, consisting of starkly dramatic black-and-white photos that capture the eerie, timeless beauty of such places as Machu Picchu and the dead city of Pacatnamu. Milne's book is simply splendid. Glorious color, sensitive prose, and marvelous images fill every page. The reader cannot help but be moved by the simple grandeur and majesty of these 140 sacred places, and there is more to come; this ambitious work is the first volume in a projected series. Either titles would enhance any general collection; to have both would be ideal.

Judith F. Bradley, Acad. of the Holy Cross Lib., Kensington, Md.

Stonehenge and Avebury and neighbouring monuments; an illustrated guide
Richard John Copland Atkinson (Author), London: H. M. Stationery Office, 1959

Stonehenge Decoded
Gerald Hawkins, London: Souvenir Press, 1966

The Making of Stonehenge
London and New York: Routledge, 1993

On Stonehenge
Fred Hoyle, San Francisco: W. H. Freeman and Company, 1977

Echoes of the Ancient Skies : The Astronomy of Lost Civilizations
E. C. Krupp, New York: Harper & Row, 1983

Stonehenge and Other British Monuments Astronomically Considered. 
Sir Norman Lockyer, London: Macmillan, 1906

Pi in the Sky: A Revelation of the Ancient Wisdom Tradition
Michael Poynder, London: Rider, 1992.

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The Stonehenge Codes, New Light on Ancient Knowledge? - by Professor David Gregg
Professor David Gregg, stonehenge, stonehenge design, stonehenge geometry, astroarchaeology, ancient astronomy, megalithic yard, golden section, eclipse prediction, Professor Thom, ancient metrics