The language of geometry is universal, and I have it shown it takes hundreds of words (actually thousands) to explain the design of the Coffer. A picture tells a story as they say.

My last post was not based on number crunching, and came to me just last night, but I saved my analysis for this morning. There may be a blunder in there somewhere, but I adopted 20/9 digits as the design some weeks ago, if not many weeks ago.

I just got a picture in my head that the rebate created cubes in the corners which might have some significance. Most of my pyramid theories are actually geometric pictures which I tested against the measurements.

What got me hooked was that the vertical and perpendicular height of the Grand Gallery squared the circle. I recall turning over a set square at school again and again, rather bored, but fascinated by how turning the triangular over created two parallel lines separated by a perpendicular and vertical height.

Thirty years later I took the train to London to find out the measured height of the gallery from Smyth vol 2, and found that it was indeed very close indeed to theoretical height of the square root of 280 in cubits. I couldn't understand how Petrie, Smyth et al had overlooked such a simple geometric design. Smyth thought the design height of the pyramid was 282 cubits, assuming he bothered to calculate the height in cubits, and Petrie proved it was 280 cubits

I hoped for a measured height of 344.9 inches using a conversion factor of 20.61 inches per royal cubit, and the first three measurements taken on the sloping floor near the north end were 344.2 inches, 343.7 inches and 344.6 inches so the average near the north wall where construction started equates to 344.6 inches.

I was not actually the first to suggest the vertical height represented the square root of 280 in cubits, but I was the first, as far as I know, to explain its significance having been quite inattentive at maths at school.

A huge treasure has been lost from the Coffer because Petrie disputed Smyth's theory of its geometric design. It seems likely that the treasure will never be recovered such is the admiration for Petrie among Egyptologists.

I once attended a conference chaired by Petrie's granddaughter, L. Petrie, who announced that she was indeed Petrie's granddaughter, and not surprisingly - rightly so - the reaction of those present was one of awe if I interpreted the body language of those present correctly. One of the speakers mentioned pyramid theories, and the smiles of derision were on faces all around me. The truth is that the division between Smyth's supporters and Petrie's supporters cannot be bridged.

Smyth had proposed that the pyramid squared the circle with respect to area, but Petrie argued that the design only squared the circle with respect to the ratio between the circumference and diameter of a circle. Many Egyptologists like Dr Lightbody appear to accept Petrie's Pi theory, but as far as I know none are vocal about Smyth's Pi theory. I stand to be corrected.

The design of the Coffer is easy to understand compared to the Grand Gallery. The sloping floor of the gallery rises by the side length of a square if twice the diameter of any circle is projected on the floor of the gallery. The geometric model is exact for the Pi approximation 22/7 assuming a design height (vertical) equal to the square root of 280 in cubits and a perpendicular height of exactly 15 cubits.

The virtual triangle in the soaring elevations of the gallery can be flipped over to yield the slope of the floor as if it was a virtual set square. The angle is equal to a horizontal displacement of 15 cubits for a slope length equal to the square root of 280 in cubits.

Smyth proposed that the angle of the sloping floor squared the circle. Petrie accepted that the observed angle was very close to the theoretical angle, but rejected the theory.

Smyth seems to have been at the peak of his powers when he developed his pyramid geometric theories, as judged by his contributions to spectroscopy in the 1870's. His obituary in the notices of the Royal Astronomical Society commented that his observations had been largely interspersed with mystical speculation much to the prejudice of their scientific value.

If you can overlook the prejudice then you will find that Smyth's report of his observations is perhaps the first very precise survey of an archaeological object with many measurements taken to a hundredth of an inch.

I now prefer Lauer's cubit of 524 millimetres which I found in a journal at Liverpool University, but failed to note a reference. If I had a name like yours then I would probably read J.P. Lauer.

20.63 inches = 524.00 millimetres to 2 decimal places

Mark