wiki on Thuban:

"It was closest to the pole in 2787 BC, when it was less than two and a half arc-minutes away from the pole."

This means that the diameter you refer to is actually less than 5 arc-minutes.

This is probably the actual position and not the phenomenal one can find in astronomic programs like Starry Night.

My program yields an alignment date of 2799 BC but an angle of 6 arc minutes. Double this is 12 arc minutes. But why should we have to double it?

Another solution{Petrie data}:

arctan[{+0.45"+0.55"-(–0.46")-(–0.5")}/245.1"] = arctan[(227.47"-225.51")/245.1"] = 27' 29.4"


Declination = 90° - 27' 29.4" = 89° 32' 30.6"