Watch the sky for a couple years and mark the spot where the star comes up and goes up and then goes down - split the difference and wallah, you have an approximation of north
For Don
Took that math problem to Bad Astronomy and got this one response which might answer your question.
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I'll give it a shot. (post from Kristophe)
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.....In my wanderings and studies I chanced upon studying the tilt of the Earth's axis and related topics and then I noted a line at Giza which I thought should go 45 degrees and then it hit me. Why do the pyramids face North ?
That is to say why do they hit North of the present day ?
They were built a minimum of 4500 years ago? ... Should they not hit North of that era ?
The North of today and the North of 4500 years ago are the same. The Magnetic North Pole and the Celestial North Pole change with time, but the Geographical North Pole does not.
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Using calculations that translates to the shift:
41000 = 1.5 degrees (24 - 22.5 agreed maximum and minimum tilt)
I assume 41,000 is supposed to be the number of years in the cycle of the Earth's axial tilt. A quick look at Wikipedia suggests that the numbers should actually be 24.5 - 21.5, which gives a difference of 3, not 1.5.
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This is a cycle so divide by 2
1 yr = 1.5 / 20,500
4500 yrs = 4500 x (1.5 / 20,500)
4500 yrs = 0.08 degree = 28.8 minutes ( I think my math is correct)
Using 3 instead of 1.5, I get 39.5 minutes.
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However apparently the pyramids are only 5 minutes off due North and even this Petrie writes is very noticeable.
Why is the deviation not 28.8 minutes ?
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It's not 28.8, nor is it 39.5, because there's no reason for it to be. The real question is "Why is the deviation not 0?" It would have been easy enough for the Egyptians to find geographical north, and that doesn't change with time. If the pyramids are only off by 5 minutes, then that's probably due simply to error in measurement of where north is.