Perhaps the most famous and best known of all the architectural constructions of the ancient Egyptians are the pyramids, the Great Sphinx, and the Temple of Karnak. And of the 80 or so pyramids, there is no doubt that the Great Pyramid of Khufu (in Greek, Cheops), which was built during the Fourth Dynasty (c. 2644 B.C.), is the one which has most stirred the thoughts and fired the imaginations of all interested in ancient Egypt. Authors, novelists, journalists, and writers of fiction found during the nineteenth century a new topic, a new idea to develop, and the less that was known and clearly understood about the subject, the more freely could they give rein to imagination and invention. These writers were forerunners of the American, Edgar Rice Burroughs, who created the fictional character Tarzan of the Apes, and set him up in central Africa, a country Burroughs had never visited and knew nothing about. Burroughs let his imagination run riot, and his novels (translated into fifty-six languages) achieved sales that were exceeded only by the Bible and Euclid's Elements.
Many writers have propounded theories on the origins, the mathematical properties, and the pseudo-astronomical marvels of Cheops, and further, made extravagant prophecies about the Great Pyramid. A resurgence of this cult occurred when Carter discovered the tomb of Tutankhamen in 1923, so that these fictions were presented all over again to the general reading public. Some of them still live on!
It may therefore come as a surprise to those readers with whom any memories remain of those "wonderful disclosures" that most of the miraculous stories written by these writers have no foundation in scientific fact at all; that the remarkable mathematical properties attributed to the Great Pyramid measurements are nowhere attested by scholarly Egyptological studies. It is only because they then were, and perhaps still are, so widely distributed and accepted that any reference to them at all is made in this book. And if some long-cherished illusions are thus destroyed, it is simply because they truly deserve to be destroyed, as being entirely contrary to fact, to history, and to truth.
Among the extraordinary things claimed by these writers, one can read that Piazzi Smyth asserted that half the distance round the square base of the Great Pyramid divided by its height was exactly equal to Pi, the ratio of the circumference to the diameter of a circle; and that 1/360 part of the base equals one five-millionth part of the earth's axis of rotation, whatever that might mean !
Even such a sober-minded person as H. W. Turnbull writes, "Their land surveyors were known as rope stretchers, because they used ropes with knots or marks at equal intervals to measure their plots of land. By this simple means, they were able to construct right angles, for they knew that three ropes of lengths three, four, and five units respectively, could be formed into a right~angled triangle."
It is, however, nowhere attested that the ancient Egyptians knew even the very simplest case of Pythagoras's theorem! But Turnbull goes further: "As Professor D'Arcy Thompson has suggested, the very shape of the Great Pyramid indicates a considerable familiarity with that [sic] of the regular pentagon. A certain obscure passage in Herodotus, can, by the slightest literal emendation, be made to yield excellent sense. It would imply that the area of each triangular face of the Pyramid, is equal to the square of the vertical height. If this is so, the ratios of height, slope, and base, can be expressed in terms of the golden section, or of the ratio of a circle to the side of the inscribed decagon."
I am unable to understand exactly what Turnbull means by this last sentence. But whatever it means, with further slight emendations, the dimensions of the Eiffel Tower or Boulder Dam could be made to produce equally vague and pretentious expressions of a mathematical connotation. I am also unable to locate the reference attributed to D'Arcy Thompson. I would say it is certainly not in his well-known "Growth and Form." Nor can I locate the "certain obscure passage in Herodotus," to find out what this slight "literal emendation" might be.
Anyone wishing to look further into this pyramid mysticism should refer to Leonard Cottrell's The Mountains of Pharaoh, whose Chapter 11 is titled, "The Great Pyramidiot," meaning Smyth but which refers also to John Taylor, Rev. John Davidson, and Edgar Stewart. For a readily available text, The Pyramids of Egypt, by I. E. S. Edwards of the British Museum, can be consulted.