Review of Tom Napier's Pyramid Speech
Program review: "The Two Mysteries of the Great Pyramid" -- Newsletter editor Tom Napier presented "The Two Mysteries of the Great Pyramid" to 31 people at the Bensalem Branch of the Bucks County Library on Saturday, January 27.
Tom started his lecture by relating how his longtime interest in ancient history led him to Egypt. While in Egypt he got a first hand look at the pyramid of the pharaoh Khufu, also known as the Great Pyramid. Tom explained that the Great Pyramid has no surviving instructions on how it was built, therefore information on how the pyramid could have been built has to be inferred through records of how other monuments were built, and through archeology. Based on the records of other monument building, Tom showed how a team of approximately 4000 full time employees could have been used to cut and move stones for the Great Pyramid. These workers were likely to have been helped by thousands of farmers during the spring flooding of the Nile. When the Nile flooded, giant stones could be transported on rafts from sites upstream. Archeological evidence has shown that earth ramps were used to place the stones once they arrived on the site.
Tom also spoke of the myth that the Great Pyramid was the first one built and that the rest were poor imitations. Evidence has shown that pyramid building was a process that evolved from the simple pyramid of Djoser at Saqqara to the Great Pyramid at Giza. Next Tom speculated on a motive to build the pyramids. Studies of ancient Egyptian religion have shown that the builders were motivated by a dream --- they believed in an underworld where they could go after death. Once the pharaoh died he could bring the rest of his people with him! Thoughts of immortality drove the pyramid building craze. With information on construction and motivation, Tom considered the first mystery of the Great Pyramid solved.
The second mystery of the Great Pyramid came about in modern times. In 1683 a man named John Greaves made measurements of the pyramid and, since that time, people have had some very odd ideas about the Great Pyramid and pyramids in general.
There are four ideas about pyramids that are common in the modern era. One started in 1859 when John Taylor related the Great Pyramid to Biblical prophesy. The prophesy predicted the end of the world and can still be seen in modern publications.
The second idea is that the Great Pyramid has advanced mathematical properties built into it that the ancient Egyptians were not capable of. This idea started with Charles Piazzi Smyth who thought the pyramids were divine measures of time. It continues with the present day speculators who feel that the pyramids were built by ancient astronauts or Atlanteans.
The third idea is that the Great Pyramid was a giant observatory. Much of this is related to mathematical manipulation that supposedly shows a connection to the stars.
The final idea is that the pyramid shape in general has magical properties such as the uncanny ability to sharpen a dull razor blade.
Tom demonstrated how none of these ideas has withstood scrutiny. Therefore the second mystery of the Great Pyramid is simple. Why do we need to create a new mystery to replace an old one? With this the audience gave Tom an appreciative hand for a program well structured and presented. Upcoming Program Meetings are held at the Bensalem Branch of the Bucks County Free Library Bringing UFOs Down to Earth. Saturday March 23, 1.30pm (Note early start!) For 35 years Philip Klass has been a senior editor with Aviation Week and Space Technology magazine. He is recognized as the world's leading skeptical authority on Unidentified Flying Objects. He is the author of UFOs: The Public Deceived and UFOs Explained and will be answering questions such as: What are UFOs? Are they extraterrestrial craft visiting Earth? Are they abducting thousands of innocent citizens and subjecting them to traumatic indignities? Did a flying saucer crash near Roswell, NM nearly 50 years ago? Has the US government managed to keep that event under cover?
Note: We have the following additions from Tom:
To seamussava@arrakis.es from Tom Napier via eric@voicenet.com March 13, 1997
Dear Seamus,
Eric has passed to me your comments on the design of the Great Pyramid so I thought I would tell you what I found when I was preparing a lecture on pyramid mythology in 1989. One of the myths I examined is the one which says that the ancient Egyptians had designed Khufu's pyramid to enshrine their discovery of the value of pi. What follows comes from a paper I wrote explaining why this was not so.
A connection between pi and the Great Pyramid was first mooted in 1859 in the book, The Great Pyramid: "Why was it Built and who Built it?" written by John Taylor, a London publisher. He noticed that twice the base of the pyramid, divided by its height, was approximately equal to pi. Despite the poor quality of the available measurements he declared that this ratio was exactly equal to pi and that it had been deliberately incorporated into the design.
In 1880 Flinders Petrie, the first real archeologist, went to Egypt armed with the most accurate instruments then available. His measurements confirmed that, whether by accident or by design, pi could indeed be derived from the dimensions of the Great Pyramid. There is no direct evidence that the builders of the Great Pyramid knew the value of pi. Over a thousand years later, the earliest time from which we have a recorded value of pi, the Egyptians were using three and an sixth or three and an eighth, neither particularly close to the correct value. There is a simpler explanation of the proportions of the pyramid but it does not seem to have occurred to anyone until the mid 1980s. The slope of the Great Pyramid, which determines its base to height ratio, is about 51 degrees 50 minutes. Why, since pyramid angles vary quite widely, was this particular value chosen? Naturally Egyptian architects knew roughly how steep they could make a pyramid before it would crumble under its own weight but they faced the practical problem of making the finished pyramid conform to the plan. The slope is controlled by the placement of the first row of stones in each new layer. How would the designers tell the laborers where to place that row? Obviously it had to be set back a bit from the previous layer but how far back? Out comes the measuring stick. It is a royal cubit long and is divided into 28 fingers or inches. Measure up one cubit and inwards 22 inches, that is where the next stone should go. Up one 28 inch cubit and in 22 inches gives the slope of the Great Pyramid almost exactly. If the slope of the Great Pyramid was indeed determined in this manner then the ratio of twice its base to its height would be exactly three and a seventh which is, coincidentally, not too bad an approximation to pi. That the slope can be represented by an integer ratio proves nothing, it might be as much a coincidence as the value of pi.
The obvious next step is to examine the angles of some other pyramids. There is a slight problem here since one has first to find published figures and then to estimate their reliability. Only on the Great Pyramid has it been possible to determine the original slope from measurements on sample casing stones. Many books give pyramid angles but for the most part they copy from the same earlier sources. Where they do not disagree amongst themselves they quote values tracable, in some cases, to Petrie's original 1880 measurements. Slopes are often quoted to within seconds of arc. This precision is a spurious one produced by averaging several rougher measurements. The only measurement I found which had an error estimate was Petrie's figure for the north face of the Great Pyramid which was 51° 50' 40" plus or minus 1' 5". Using the best numbers available I first tried earlier pyramids such as the northern pyramid at Dashur and the Bent Pyramid. The Dashur pyramid has a gentle slope, 43 degrees 40 minutes. Its setback is about 29 and a third inches for each cubit of height, not too good a fit to my theory. The designers of the Bent pyramid were ambitious and started off with a much steeper slope, 54 degrees 31 minutes. This is exactly equivalent to "up a cubit and in 20 inches." Halfway up they changed their minds, the upper part has a setback of about 29 and two-thirds inches, again this does not confirm the theory. Khafre's pyramid, built later than Khufu's, is a little steeper, its setback is exactly 21 inches per cubit. Two later pyramids, those of Menkure and Sahure have a setback of 23 inches per cubit. Of all the slopes I could find, of pyramids built over a period of three hundred years, most agreed exactly with the 28 inch cubit system. Only the slope of the northern pyramid at Dashur and the upper slope of the Bent Pyramid did not. As it happens these have slopes given by 22 inches in for every 21 inches up and 18 inches in for every 17 inches up so it looks as if even the exceptions indicate that the Egyptians used simple whole number ratios to determine the slopes of their pyramids.
Each of the latter two ratios is a number divided by second number which is one greater than the first. We know that the Egyptian system of fractions used only the reciprocals of integers thus these ratios would have been described as a cubit and the 21st part of a cubit or a cubit and the 17th part of a cubit respectively. This table summarizes my findings - Inches Calculated Pyramid Difference Pyramid per slope slope (minutes) name cubit d m s d m s 20 54 27 44 54 31 13 +3.5 Bent 21 53 07 48 53 10 +2.2 Khafre 22 51 50 34 51 50 14 -0.3 Khufu 23 50 35 58 50 36 0.0 Sahure An inch difference in the setback makes more than a degree of difference in the slope. Both the difference between the calculated and measured slopes and the probable error in the measured slopes are a few minutes of arc. This represents about a twentieth of an inch error in the setback and seems to confirm that at least four (and probably five) pyramids were built using this method of measurement. Note that every whole inch from 20 through 23 has been used somewhere on a pyramid. Khufu's falls in the middle of this range and thus just happens to approximate pi.
It is clear that the slopes of the pyramids were based on such practical engineering considerations as the strength of materials and the number of inches in a cubit. As an illustration for my lecture I made a right-triangular "pyramid gauge" from three strips of wood. It was fitted with a plumb-line so that when one corner was placed on a row of stones and the plumb-line was lined up with a mark on the hypotenuse, one side was vertical and one side was horizontal. The hypotenuse indicated the slope and thus the position where the next row of stones would go. I was rather gratified when, some years later, I noticed a very similar wooden triangle and plumb-line device on display in an Egyptian museum shown on TV.
I hope this is of some use to you
Tom
PI and the Pyramids
Many people make a great mystery out of the mid-nineteenth century discovery that if you divide twice the base of the Great Pyramid by its height you get an approximation to pi. They leap from this likeness to the conclusion that the Great Pyramid was built with the sole intention of celebrating pi. They overlook that the ancient Egyptians built about 70 pyramids over a 300 year period. None of the others which remain measurable celebrate pi but collectively they reveal why the Great Pyramid apparently does. The relationship between pi and the dimensions of the Great Pyramid is an artifact of the construction process.
As a physicist, engineer and occasional lecturer on pyramid myths I knew there was no historical evidence that the pyramid builders even knew the value of pi. The earliest documented (but incorrect) Egyptian value dates from a thousand years later. Can we, using Occam's Razor, find a simpler explanation?
The slope of the Great Pyramid, which determines its base to height ratio, is about 52 degrees. Why was this particular value chosen from the range of practical slopes? Obviously the slope was measured during construction to ensure that it remained constant. If the measurement was done in royal cubits, which were divided into 28 fingers, then the slope of the Great Pyramid conforms to, "Measure up one cubit and inwards 22 fingers." This makes the ratio of twice the base to the height exactly three and a seventh, not too bad an approximation to pi.
That the slope can be represented by an integer ratio proves nothing; it might be as much a coincidence as the appearance of pi. However, on examining the slopes of other pyramids I found the majority of them conformed to the same algorithm. The vertical measurement was one cubit and the horizontal measurement was an integer number of fingers.
This table summarizes my findings -
Setback Calculated Pyramid Difference Pyramid
(fingers) slope slope
(minutes) name
d m s d m
20 54 27 44
54 31 +3.5
Bent (lower)
21 53 07 48
53 10 +2.2
Khafre
22 51 50 34
51 50 -0.3
Khufu
23 50 35 58
50 36 0.0
Sahure
23 50 35 58
50 47 +11.0 Menkure
Every integer number of fingers from 20 through 23 has been used somewhere. The Great (Khufu's) Pyramid, falls in the middle of this range. Other slopes on the Great Pyramid were probably measured by similar means. For example, while the Descending Passage might have been aligned on the pole star, then Alpha Draconis, it is much more likely that its 2:1 slope results from practical measurements. It is clear that the dimensions of the pyramids were based on such considerations as the strength of materials and the number of fingers in a cubit and have nothing whatsoever to do with occult knowledge.
Copyright (c) 1992 Tom Napier