"Squaring the circle" refers to the problem of taking a given circle and constructing a square with the same area. One was probably limited to just using a straight-edge and compass.

The site you gave was using this as a play on words, as the curved lines of the orbits about the north star blend into the ends of the lines marking each layer of the step pyramid (the base of a pyramid being a square).

There are three issues with the claim:

1. It's not all that miraculous that the ancients would know what North is.

2. Precession. The earth doesn't just rotate on its axis. It wobbles. The wobbling has a long period, but over time the north star changes. Unless the step pyramid is mounted on a swivel, it's not likely that the picture looks so obvious as what the portray. (I think the ancient egyptians considered alpha draconis - and not Polaris - as the North Star.)

3. The concentrentric circles they draw to illustrate their point just happens to be through stars whose "orbits" take them into the edges. Considering the number of stars in the night sky - particularly in those ages before urban light pollution - it would have been much more impressive had they noted that those "orbits" were absent of stars.



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