## Pi and the Great Pyramid

People seem to think that it is amazing that dimensions of the Great Pyramid might be related to pi. Evidence of ancient astronauts? In (pi), I said this:

I hear that the dimensions of the Great Pyramid (of Khufu, also known as Cheops) show that the ancient Egyptians knew the value of pi. Those people who measure the dimensions of pyramids claim tremendous accuracy, much more accuracy than the rough exterior of a pyramid warrants. So, when they say that the Great Pyramid exhibits the value pi, to many decimal places, a person should be skeptical. But, it is also not very remarkable that the ancient Egyptians might have used pi in this pyramid. It seems that the base (much of it is missing) of the pyramid is within a few inches of being square, and is just a few minutes of arc from being aligned with true north, very accurate indeed.

By the way, there are many pyramids, and each has a different slope. So, the Great Pyramid is the only one with just those dimensions and ratios (one of Seneferu's pyramids is close). There is also evidence that the ancient Egyptians preferred a steeper slope than that of the Great Pyramid, but had to settle for shallower slopes, to keep the pyramids from collapsing.

The ancient Egyptians seem to have sometimes used a value of 22/7 (3.142857 . . .) for pi. There is also evidence that they estimated the area of a circle with a square with a side that is 8/9 the size of the circle's diameter. This gives a value of pi of 3.16049382716 . . .

Any fool can figure that the value of pi is a little greater than 3, if he/she wants to experiment a little. Draw a circle, the larger the better, and measure the diameter and the circumference (with a string perhaps). Calculate pi=C/2r. You will probably get 3 or 4 digits of accuracy. If you are really good at that sort of thing, you may be able to get 5 digits. That's pretty good. That's better than Archimedes' estimate. Try that for a simple low-tech science fair project.

Pi is approximately 3.1415926535 . . . Concerning Khufu's (Cheops') Great Pyramid, twice the length of one side, divided by the height, is approximately pi. The published dimensions vary, depending on the sources, and so the accuracy of any relationship with pi also varies (from errors in the inches (or centimeters) to a few feet (many centimeters)). This relationship may be a coincidence. And, as I said above, knowledge of pi is not very exciting. And the more or less accidental use of pi, measuring distances with a wheel perhaps, is also possible. After all you don't need to know the value of pi to use a circle.

Some people also seem to be amazed that pyramids are found in other parts of the world. On the other hand, they are probably not amazed that rectangular buildings have always been popular. A pyramid is a relatively simple shape. Only a tetrahedron (triangular pyramid) has fewer sides. I think that it would be amazing if only one culture made buildings of such a simple shape. The Central American pyramids were built thousands of years after the Egyptian pyramids; they are much smaller; they are much flatter (they don't look like Egyptian pyramids); their purposes (what can be deduced of their purposes) were vastly different.

I. Edwards of the British Museum has this to say about people who believe strange things about the pyramids:

They are known as "pyramidiots." And of course these people know absolutely nothing about archeology of the major pyramids. These structures are royal tombs, simply one element in a whole complex of buildings, all of which were related in their funerary purposes.

In my article on Golden Rectangle and Golden Ratio, I have added this paragraph:

I was just watching the award-winning, short documentary, Fibonacci and the Golden Mean. And they had the first diagram on the right, claiming that the builders of Khufu's (Cheops') Great Pyramid incorporated the golden mean into the pyramid. A little arithmetic shows that the diagram is wrong. What they should have drawn was the second diagram on the right. The ratios in the red triangle are very close to the golden ratio. See Pi and the Great Pyramid [this article], where we find that the Great Pyramid also exhibits the ratio pi. If the designers of the pyramid meant to use pi, then it is merely a coincidence that the golden ratio crops up (as any pyramid that shows pi in that way will show the golden ratio, approximately). And vice versa, if they meant to use the golden ratio, then it is a coincidence that pi appears.

One book claims to give the original lengths of the sides of the Great Pyramid to within 1/10000 of an inch. I consider such a claim to be an outright lie. Here are the dimensions given in that book: west side=755 feet 9.1551 inches, north side=755 feet 4.9818 inches, east side 755 feet 10.4937 inches, south side 756 feet, 0.9739 inches, height=481.3949 feet (not quite as accurate, but still in the range of fantasy). That makes the perimeter of the base 3023.133708 feet, and the estimate of pi is 3.139973. That is not a very good estimate of pi, in my opinion. [These dimensions give a value of phi of 1.622812 for the golden ratio, by the way. The actual value is 1.618034]

One book claims that you would need a laser theodolite to align something north/south with the accuracy that the Great Pyramid shows. A laser theodolite will never help you align anything north/south unless you already have a north/south reference line somewhere. The only way to create a north/south reference line from scratch, then and now, is to accurately observe the stars.

Another claim is that the Great Pyramid is positioned almost exactly one third of the way from the equator to the north pole, in other words on the 30 degree line of latitude. It is very close to that, about a mile or two. But so was Memphis; so is Cairo. It is certainly possible to locate a monument on the 30th parallel, by studying the stars. But it can also be another coincidence. We are also told that the Great Pyramid is at the center of a circle defined by the Nile Delta (see Map of Ancient Egypt). Again, so are Memphis and Cairo; and the people who claim this usually redraw the delta to look even more circular than it is. The positioning of the Great Pyramid probably had plenty to do with the fact that it rests upon exposed bedrock, and it is near a rock quarry.

Those who believe in strange and amazing things about the great pyramid call themselves "pyramidologists," who hypothesize about "pyramidology." One book by such a person gives the perimeter (pyrimeter?) of the pyramid as 921,453 mm. Converting to "pyramid inches" (See The Pyramid Inch), he gets a perimeter of 36,239.2895 pyramid inches. He actually gained three digits of accuracy by converting units. See Superfluous Accuracy.

See My Pyramids.