Thoughts on past travellers

Herodotus and the pyramid of Cheops

by Giorgio Agnese

There are many translations of Herodotus’ writings on the great pyramid in Giza in “HISTORIAE” (II – 124) and different interpretations of them have left space for many doubts and imaginative theories.

The dimensions of the pyramid have themselves been the subject of mathematical and numerical calculations, with some highly creative “pyramidologists”, practising the worst form of Egyptology, rising to fame with connivance of the press.

For those interested in the subject, I will try to give a reliable translation of the Greek text in the light of geometrical knowledge at the time. Herodotus states that every mètopon (side, face, front) of the pyramid of Cheops measures 8 plethra (òcto plethra), specifying that the base is square (tetràgonou). As the plethrum was a linear measurement corresponding to about 30 metres, Herodotus means that the length of one side of the base was about 240 metres, not far off the actual figure (230.3 m).

He then adds … of equal height (ùpsos ìson)…, by which he means more logically the apothems (the height of the triangles which form the faces of the pyramid) rather than the height of the pyramid itself. Here he was less accurate, as the apothem of the pyramid is about 186 metres (if he was in fact referring to its height, he would have been even more inaccurate, as the actual figure is 146.5 m). Nevertheless, he can certainly be forgiven as he probably didn’t climb to the top of the pyramid to measure it, nor did he calculate it, and even today the visual estimation of vertical heights is very difficult.

Of course numerous reports by subsequent visitors give, more or less accurately, measurements of the base and height, as they are the easiest for readers to understand. It is therefore seems unlikely that Herodotus would have devised a complicated relationship between the surfaces of Diophantus triangles [NB: For non-experts, Diophantus was a Alexandrian Greek mathematician who lived in the II century, best known for his treatise on mathematics and second degree equations.], as some researchers have sustained, as well as their being no mention of this in the Greek text!

Rather than a historian, Herodotus should be considered as a curious chronicler, reporting both on what he saw personally, as well as on the information he received when he visited Egypt in about 450 BC, then under Persian domination. He gathered information on the history of Egypt by interviewing the priests who were the custodians of knowledge at the time. While he had the honesty to tell his readers when he was unconvinced by certain assertions, he was not always able to distinguish historical fact from historical fiction about events which had occurred dozens of centuries previously. His work contains frequent mistakes and errors, but in general it’s content was and continues to be of vital importance for research in the field of Egyptology.

The Great Pyramid has been measured and re-measured numerous times in the last two centuries and our only possible reaction to the reliable and accurate inside and outside measurements now available is one of amazement at the design and construction skills of the Egyptians of 45 centuries ago!

Facts and figures about the pyramid

It is a nonsense to state that the calculations made using the pyramid’s measurements “are exact to three decimal places” as some pyramidologists sustain (without of course specifying precisely which reference they use!), because the lengths of each side vary at the first decimal point.

However, it is true to say that the surface areas of the pyramid’s faces are “almost” equal to those of the square on its height (230,3×186,4 : 2 = 21.463,9 square metres vs. the square 146.5×146.5 = 21.462,25 square metres).

The theoretical height is considered to be 146.58 m (280 cubits), but there are those who believe that the pyramid was not finished with a point but with a platform (today at a height of 139 m measuring abt. 10×10 m) which, being smaller, may have been situated even higher in the past.

Nevertheless, we cannot help but accept that the surface area values are a very good approximation and the possibility that this is the result of chance can be excluded.

Even the straightforward relationship between half the perimeter of the base and the height represents an excellent approximation of pi (the height corresponds to the radius of a circle with circumference equal to the perimeter of the pyramid: with the measurements expressed in cubits, H = 280, L = 440, we have 880 / 280 = 3.1428…). The measurements of the funeral chamber, the sarcophagus and other dimensional relationships and concatenations which can be found in the architecture of this pyramid, so unusual compared with all the others found in Egypt, cannot help but be the subject of serious reflection.

Born on 22 November 1938 in La Spezia, Giorgio Agnese lives in Genoa, where he studied humanities at school and graduated in electrical engineering from university.

He began his career in Milan, contributing to major projects in Italy and worldwide. He is now retired and an industrial consultant.
He is a member of the Egypt Exploration Society of London and Director of the Genoa Archaeological Group. His interest in archaeology, which dates back to his school years, is addressed to studying the origins of the ancient civilisations and in particular the Egyptian civilisation. His studies focus particularly on the historical/chronological reconstruction from recent archaeological discoveries of the Ancient Kingdom and the pre-dynasty period. He is particularly interested in the technologies used in the production cycles of architectural works in the period.