The Great Pyramid of Giza is remarkable not only as an architectural marvel. The four sides of its square base are in almost perfect alignment with the cardinal directions, just a fraction of a degree off, counter-clockwise, from the true geographic north, south, east and west.
Two other monuments, the neighbouring Pyramid of Khafre and the Red Pyramid at Dahshur, follow a near-identical alignment, with each one a different fraction of a degree counter-clockwise from the cardinal directions. When the ancient Egyptians built the Great Pyramid four-and-a half millennia ago, they had no access to modern equipment such as a magnetic compass – which would have pointed towards the magnetic north, with a declination from true north. So how did the Egyptians manage such accuracy?
Theories abound. Some scholars suggest the Egyptians used calculations based on observations of the pole star. Others suggest their calculations were based on observations of the stars Kochab ( b-Ursa Minor) and Mizar (z-Ursa Major).
Then, there is also the theory with an Indian connection. The ‘Indian circle’ method is a long-established surveyor’s tool for determining east and west. Although its earliest known description is in the Vedic text, Katyayana Sulba-sutra, written in 400-300 BC, the method is believed to have been in use in the east-west alignment of Harappan structures as far back as the second millennium BC, possibly even earlier elsewhere. One theory suggests that the ancient Egyptians followed a similar method to determine east and west when they built the pyramids.
Now, a researcher has proposed a variant — with no strings attached. The method Katyayana describes includes a string tied to a rod. Glen Dash, an American engineer who runs a charitable foundation for archaeology, has done away with the string in a method he describes in The Journal of Ancient Egyptian Architecture.
It comes with a restriction, though. The Indian circle method works on any sunny day. The method Dash credits the ancient Egyptians with, on the other hand, will be perfect only once a year, the autumn date when the day and the night are of nearly equal duration. Called the autumnal equinox, this date varies between September 21 and 24 from year to year.
So how do the method and its variant work? To use the Indian circle method, strike a rod into the ground, upright, and observe its shadow. As the sun moves across the sky, so will the shadow of the rod, through the day. At regular intervals, mark the position of the tip of the shadow. This will plot out a smooth curve, known as the shadow line.
At the end of the day, tie a string to the rod, hold it taut and rotate it around the rod. This will describe a circle. The two curves — shadow line and circle — will intersect at two points. Draw a straight line through these two points; it will run east-west.
Dash introduces a variant he calls the “equinoctial solar gnomon method”; “gnomon” is the rod. “On the equinox, the surveyor will find that the tip of the shadow runs in a straight line and nearly perfectly east-west,” he writes. “Since the shadow line is already straight and already runs east-west, the second step… drawing a circle around the gnomon, is not needed.”
That is theory, which Dash put into practice at his home in Connecticut on the equinox of September 22, 2016. His experiments returned an alignment that was nearly east-west, only slightly counter-clockwise. “The magnitude and direction of these errors suggest that it is possible that all three pyramids were aligned using the equinoctial method on the autumnal equinox,” Dash writes.
Although the Indian circle method was described centuries after the pyramids were built, could the Egyptians not have used it too? “It is certainly possible that the Egyptians could have used the Indian circle method. They could have then found due east-west without waiting for the autumn equinox,” Dash told The Indian Express, by email. “However, waiting until the equinox has two advantages. First, the method is simpler, the gnomon (vertical rod) used does not have to be straight, just well fixed, and second, the slight error you get more or less matches the error you actually see at the largest of the pyramids,” he said.
In the study, he writes: “As to the methods they actually did use, the Egyptians, unfortunately, left us few clues.”