I knew I'd seen this picture before (Plimpton tablet 322). The 1948 book "Number Theory and its History", by Oystein Ore of Yale, has a picture of the tablet on p. 175, and discussion nearby, identifying it as a trig table of angles 45 to 31 degrees, with a spacing of about 1 degree. Ore refers to Neugebauer & Sachs' 1945 paper about (catalog of?) the mathematical Plimpton tablets. My impression is that Ore is the originator of the trig-table interpretation, but I haven't looked at the N&S paper. Ore notes that finding integer right triangles with roughly 1-degree spaced angles, and having other-legs with terminating base 60 reciprocals is not a trivial problem. He speculates about the method used. It looks like you need to find a rational number u/v near tan(45-theta/2), where u and v have only 2,3,5 as prime divisors. The entry for 45deg is 119,169; which are one leg and the hypotenuse of a 119-120-169 right triangle. In modern terms, this is the result of squaring 12+5i (=119+120i). Squaring doubles the angle, and swapping imaginary & real parts complements the angle. The imaginary leg is 2uv; restricting the prime divisors guarantees a terminating base 60 reciprocal. I only skimmed Mansfield-Wildberger, so I probably missed what they've added to the discussion. They have 30+ references, including N&S but not Ore. Rich -------- Quoting Hans Havermann <gladhobo@bell.net>:
Hm, hard to tell from the popular press I've seen about this.
The article itself appears to be online: http://www.sciencedirect.com/science/article/pii/S0315086017300691
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