Extracts from a new book,
"The Pyramid Builder's Handbook"
Derek K Hitchins©
Full copyright and intellectual property rights retained
Numerous authors have made small fortunes out of "discovering" that the transcendental number π is hidden in the Great Pyramid. This idea has arisen because of the observation that the ratio of opposite : adjacent, often used to determine slope angle, is 14 : 11. If the height of the Great Pyramid is 14 units, then half of one side is 11 units, then the periphery at the base must be 8 x 11 = 88. If you are into playing with figures, you might notice that 88 / 14 is the same as 2 x 22 / 7 and, as every schoolchild knows, 22 / 7 is a 20th century approximation for π.
So, at first glance, it looks like the ancient Egyptians "hid" the value for π in the dimensions of the Great Pyramid. Nobody seems to ask why the ancient Egyptians would hide a number exclusively associated with circles and spheres in a square-based, regular pyramid…
Ideas like this arise because people look just at one pyramid and play around endlessly with various dimensions looking for relationships. Look long enough and hard enough, and you are likely to find what you believe is there - rather like a self-fulfilling prophecy.
One way to avoid being trapped in this way is to look at all the pyramids rather than just concentrate on one - after all, as we have already seen, each pyramid has a unique slope. If the ancient Egyptians hid π in one pyramid, why wouldn't they do the same in others?
The table does the same sum that seems to produce π for the Great Pyramid, but this time it does the sum for most of the 4th-6th Dynasty pyramids. One or two do give a close approximation to π, but that should not really surprise us. It is a natural property of any typical cone or pyramid that the base periphery divided by the height will be around 3, provided the slope angle is around 50 degrees.
From the table, we would have to say that, if the ancient Egyptians knew π, then they knew it only for Meidum and Khufu, and forgot it again - twice! That seems highly unlikely. Sorry, but the whole idea is fanciful nonsense.
Moreover, such ideas obscure the more interesting, and provable, truth. The ancient Egyptians had an excellent way of measuring the area of circles, unmatched in the ancient world. The method, shown below, employs the so-called "method of squares"
If you draw out a circle on a background of small squares, as shown, then you can set it up so that the circle just touches the outer square at the four points on the four sides. Clearly, the outer square has a larger area than the circle. Now look at the inner square, formed by the pink tiles, ignoring the outer "ring" of darker, rosy tiles. Part of the circle is larger than this inner square, and this larger portion is shown in blue for just one quadrant. On the other hand, part of the inner square is smaller that the circle, and this smaller portion is shown in green for just one of the 4 quadrants.
If the blue area equals the green area, then it follows that the area of the circle equals the area of the inner square. This turns out to be the case when the area of the inner square is 8/9ths of the area of the larger square. Try it. Consider a circle of diameter 9 units. According to the ancient Egyptian formula, the area will then be (8/9 x 9)2, or 82 = 64 square units. In fact, the formula is about 0.6% accurate, quite good enough for most practical purposes. The method is outlined in the Rhind Papyrus, in the British Museum.