## Babylonian Shadow Lengths & Angles

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I think this guy should see a doctor. I don't even.

"In modern terms, the shadow lengths and time slice of the morning study would be limited by the dimensions of the "2 kus sag" chart. The midmorning shadow would at tangent angle of atan (assumed gmonon/shadow), atan (1 cubit/1 cubit), atan (1/1), 45 degrees. The understanding is that the texts define midmorning by a constant shadow length of 1 cubit, not using time. The time (after sunrise) that the sun reaches the midmorning locus varies throughout the year. At Babylon, the noon shadow from a 1 cubit gnomon varies from 9/60 to 88/60 cubits over the year. The tangent angle at noon would range from atan(1/(9/60)) to atan (1/(88/60)) , 48 to 33.86 degrees in modern terms. Assuming full scale drawing on the shadows, the 2 kus on a side would limit the "2 kus sag" chart to a certain window of shadow sizes and tangent angles. The tangent angles in the 2 kus window would be limited to atan(1/2), above 26.5 degrees. An alternate possibility is to subtract 1 cubit from the "morning lengths", which some of the gnomon instructions imply, and the resultant limit would be atan(1/(1+2), atan(1/3), above 18.4 degrees."

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Authors: ag