Go to page 11 and following before you read the text. Glen Dash is no longer with us, but if you Google his name, you'll find a very interesting individual.
http://dashfoundation.org/True_North_2013(Feb-19-13).doc
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MathTeacher; change the .doc file to a pdf file so I can read it.
John Nolton
MathTeacher;?ÿ Thank you for the conversion from .doc to pdf.
I am reading it now and will get back to you in the am.
John Nolton
It was an accidental placement.?ÿ Sort of like finding a perfectly square section that is 5280.000 feet in length on all sides.?ÿ It can happen.?ÿ The odds were 1 in 1800 of being within one-tenth of one degree.
I wouldn't start with 180 degrees. The probability distribution of someone looking at a point in the sky they know is near north and transferring it to the ground is somewhat narrow.?ÿ I'd model it as perhaps a normal distribution with a standard deviation of (take our pick) maybe a degree.?ÿ Then the odds of being within 0.1 degree would be about 0.08 or 1 in 12.
Attaboy, Bill.?ÿ You have provided a ratio far closer to what should occur.?ÿ My number was the worst possible ratio.?ÿ My number is easily cut in half by recognizing that since you are rotating a square, the worst case is pointing east to west or 90 degrees.?ÿ After that you are getting closer to north to south again.
MathTeacher; I have been going over the paper you posted and would like to make some comments.
Prof. Flinders Petrie said he thinks that the observations were made at elongation. I think that the star Thuban was tracked like Dash did in his test of the theory and with many observations (nothing fortuitous about it) you can get an azimuth of less than 1 minute. It is also to be noted that one internet search said that Thuban was closer to the celestial pole back then than Polaris is today. The internet search said that Thuban was within 10 minutes of the pole (I think Polaris is 48 minutes of the pole ).
I guess we can contact the US Naval Observatory and get some exact numbers or generate them with some astronomy software.
Thanks for the great post.?ÿ Oh one last thing; in an old surveying book I have (someplace) that was published in around 1910 or 1911 (?) the author talked about hanging a plumb bob from a limb of a tree and using a bucket of water to help steady it from the wind and then standing back with another bob and align the 2 strings with Polaris (1 minute or less). If I can find the book I will quote from the book and give the author name and correct date.
JOHN NOLTON
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It's amazing what sticks and strings can do in skilled hands. The need was there, inventions came forth, and they're still coming forth.
Consider the passage beginning on page 41 here: https://www.google.com/books/edition/The_solution_of_the_pyramid_problem/OSUAAAAAQAAJ?hl=en&gbpv=1&dq=pyramids+as+theodolites&pg=PA41&printsec=frontcover
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