Multiple Squares to form Flattened Circle Megaliths

above: a 28 square grid with double, triple (top), and four-square rectangles (red),
plus (gray again) the triple rectangles within class B


1.     Problems with Thom’s Stone Circle Geometries.

2.     Egyptian Grids of Multiple Squares.

3.     Generating Flattened Circles using a Grid of Squares.


This paper reviews the geometries proposed by Alexander Thom for a shape called a flattened circle, survivors of these being quite commonly found in the British Isles. Thom’s proposals appear to have been rejected through (a) disbelief that the Neolithic builders of megalithic monuments could have generated such sophistication using only ropes and stakes and (b) through assertions that real structures do not obey the geometry he overlaid upon his surveys.

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Introduction to my book Harmonic Origins of the World

Over the last seven thousand years, hunter-gathering humans have been transformed into the “modern” norms of citizens (city dwellers) through a series of metamorphoses during which the intellect developed ever-larger descriptions of the world. Past civilizations and even some tribal groups have left wonders in their wake, a result of uncanny skills – mental and physical – which, being hard to repeat today, cannot be considered primitive. Buildings such as Stonehenge and the Great Pyramid of Giza are felt anomalous, because of the mathematics implied by their construction. Our notational mathematics only arose much later and so, a different maths must have preceded ours.

We have also inherited texts from ancient times. Spoken language evolved before there was any writing with which to create texts. Writing developed in three main ways: (1) Pictographic writing evolved into hieroglyphs, like those of Egyptian texts, carved on stone or inked onto papyrus, (2) the Sumerians used cross-hatched lines on clay tablets, to make symbols representing the syllables within speech. Cuneiform allowed the many languages of the ancient Near East to be recorded, since all spoken language is made of syllables, (3) the Phoenicians developed the alphabet, which was perfected in Iron Age Greece through identifying more phonemes, including the vowels. The Greek language enabled individual writers to think new thoughts through writing down their ideas; a new habit that competed with information passed down through the oral tradition. Ironically though, writing down oral stories allowed their survival, as the oral tradition became more-or-less extinct. And surviving oral texts give otherwise missing insights into the intellectual life behind prehistoric monuments.

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An Angelic Geometrical Design

The above diagram contains information with can generally only be grasped by using a geometrical diagram. Its focus is the properties of a right triangle that is 4 times larger than its third and shortest side. The left hand view illustrates what we call Pythagoras’ theorum, namely that

“The squares of the shorter sides add up to the square of the longest side.”

Here this is shown as 144 + 9 = 153 because, if the third side is three lunar months long, then the 4-long base is 12 lunar months, hence the square of 12 is 144″. The longest side is then 153, the diagonal of the four squares rectangle, and the square root of 153 is 12.369 lunar months, the solar year when measured in lunar months.

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