Spaces and Places is an established letting agent with a personal touch. We have been finding accommodation for tenants in the Weston-Super-Mare area for over 20 years. We may be small but we love the challenge of joining the right tenant to the right property. When, nearly four months later, the conference broke up, the fighting still continued. Clearly Wolsey had been unsuccessful in bringing about peace, but he did not return to England empty-handed. On 24 November a treaty had been signed committing England to a declaration of war against France, at least by March 1523. Space latest news, pictures, discoveries and theories. Discover most up-to-date space information and facts.

Nick Kollerstrom is historian of science, a former honorary research fellow in Science and Technology Studies at University College, London (UCL), and a former lunar gardening correspondent for the BBC. He is the author or co-author of a number of books, including Gardening and Planting by the Moon (an annual series beginning 1980), Newton’s Forgotten Lunar Theory (2000), Crop Circles (2002), and Terror on the Tube (2009)

Strong national pressure from the Egyptian government promotes the age-old concept that three Egyptian pharaohs were responsible for constructing the pyramids at Giza. Notions of ‘scientific’ rationality argue that the pyramids ‘must’ be tombs, after all they have sarcophagi in them don’t they? Thus notions of pharaonic burial as the only ‘reasonable’ explanation combine with national sentiment for claimed ownership. Against this consensus are theories that may sound airy and vague, concerning some unknown builders using methods lost forever in the mists of prehistory.

I here argue for the latter view, and suggest that two publishing events of 2007 are relevant: documentary evidence for Howard Vyse’s forgeries in the Relieving Chambers above the King’s Chamber in the Great Pyramid, published, plus a history of ancient mathematics which endorses the integrated (mathematical) ground-plan for the three Giza pyramids, by John Legon.

Non-Egyptian Maths?

While composing the ‘Geometry of the Great Pyramid’ for the Graham Hancock Forum (1), I found myself (unexpectedly) growing more and more incredulous that ancient Egyptians could have done maths like that. For a start they did not have angular measure. How could they have appreciated the amazing properties of the Great Pyramid’s unique pi/phi slope angle without that? [NB, you might wish to read the earlier math section to refresh your memory] Instead, they had gradients for measuring slope, i.e. the ‘sekhed’. I found that slopes of the descending passages were related to those of the first and second pyramids as precise angle bisections, within an arcminute – which could surely not have been done using ancient Egyptian mathematics. Bisection of a one-seventh angle is far from being a common concept, and what would it have meant to anyone confined to sekhed measure?

The Third Pyramid of Giza has a descending passage slope angle of 26° 2′ identical within a single arcminute with that of the Great Pyramid ascending passage angle – suggesting that the same construction company built both, (2) and that the exact angle within an arcminute was intentional. This was a moderately precise angle bisection, of the outer slope angle, within about four arcminutes, and lacks a straightforward Seked value (3). The 2nd pyramid’s descending passage slope angle, generally agreed to be 25° 55,’ bisects that special angle within an arcminute.

The eternal splendour of the two great pyramids at Giza involves some kind of relationship between them, and that connection is concretely expressed by two angle bisections. The First pyramid’s descending passage angle is a simple 1:2 slope, a sekhed value of two, so its angle is 26° 33′, which bisects the slope angle of the 2nd pyramid. That used the 3-4-5 Pythagoras triangle, the first in human history. We can write that exact relationship as

That is pyramid maths! That bisection surely has to be intentional. It has to be intentional because it is symmetrical, each descending passage bisecting the other’s outer slope angle. If you only had sekheds, how could you do this?

It is widely agreed that the Great Pyramid slope angle involved a use of the 22/7 pi-approximation. (4) But Egyptian maths did not ‘square the circle’ in this manner, by equating the circumference of a circle with the perimeter of a square – only the Greeks did that, aeons later. What it did (in the Rhind Papyrus, c.1700 BC) was, to find a circle having the same area as a given square, by using an 8:9 ratio. This was equivalent to having pi as 3.16, no doubt impressive for ancient times, and books compare that to the more exact 3.14 pi value expressed in the Great Pyramid’s slope angle – however, these are very different kinds of problem; only from our modern viewpoint can we move easily between the two.

The square root of two links the Great Pyramid to John Legon’s ground-plan design. (5) The distance from the top of the pyramid to the base of the King’s Chamber, in relation to pyramid height, exactly expresses the root-two value. Egyptian units of measure contain this concept, insofar as they convert from area to linear measure, (from remens to Royal cubits) but as far as anyone knows they did not have a precise value as here used.

The height of the King’s Chamber was exactly proportioned with the sole purpose (as far as anyone knows) of placing an integer 3-4-5 Pythagoras triangle in the diagonal plane of the chamber. This ingenious 3-D structure is way outside what we know about early Egyptian math. That’s enough about math arguments, which are not everyone’s cup of tea.

The Legon Ground-Plan

We focus here upon the Second Pyramid, as having been built upon quite sloping ground, 3-6° of incline. In one corner, a huge expanse of solid rock was ‘bulldozed’ away to make a level surface, while at the other end huge cubic blocks of three metres side-length, weighing some two hundred tons each, were used to build up the level surface. That trouble could have been avoided, by moving the site a short distance, indicating that there was something vital about that location. Quoting Robin Cook, who wrote two books about the Legon ground-plan: ‘Why else build up the eastern side of Khafre’s pyramid on a giant megalithic platform when, a short distance West, it could have been founded upon natural rock?’ (6) Ralph Ellis has also commented upon how this second pyramid had been ‘countersunk into the bedrock:’ ‘The Bronze Age solution to this defect on the topography of the chosen site was ‘simple’: just form a thick raft of megalithic blocks, each weighing in at hundreds of tonnes, and then build the pyramid on top of that.’ (7) These vast blocks were finely-jointed to fit meticulously together. (8) Ellis like others discerned a stark contrast between this ‘truly astounding’ feat and construction of other, non-Giza pyramids: ‘If one looks at the third and fifth dynasty pyramids, the engineering solutions are all simple and man-manageable.’ Imaginative accounts of toiling Egyptian slaves have failed to take account of this primary phenomenon, which shifts the whole construction back into prehistory.

Why does it do that? Around the world, stand mute records of bygone ages when vast stones could be shaped, lifted, moved and fitted exactly into position in a way that later ages would find inconceivable. At Baalbeck and Jerusalem are constructions using even larger stones, carved into a rectangular block shape. The ‘Wailing wall’ of Jerusalem is one side of a vast elevated platform on which ‘Solomon’s temple’ was long ago constructed. Three titanic carved rectangular blocks in this wall each weigh in at six hundred tons. (9) They were only properly revealed following the 1967 capture of Jerusalem. We compare these with the titanic stones at Baalbeck in Lebanon, the only place on Earth with even larger stone blocks carved and fitted into a wall, of a huge flat, raised surfac

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