I picked up a book about the pyramids at Cheops. (Relax, it wasn't a crackpot work.) It said that the pyramid was aligned with the star Polaris, and that Sirus and Orion may be sighted through some of the ventilation shafts. Now the pyramid is aligned with true north. It the time of the construction of the pyramid construction, Polaris was not located at true north. This is due to the precession of the Earth's axis, which is on a cycle of about 25,500 years in period. No big deal: it is easy to find true north from the apparent rotation of the stars. However it seems to me that it is rather unlikely that Sirius would have aligned with that ventilation shaft at the time of the pyramids construction. Am I right, or is there some invariant that I'm missing? It isn't very satisfying to chalk the alignment up to "chance," but I can't come up with a better explanation.