Babylonian Trigonometry, Ahead of Its Time By Thousands of Years

In Historia Mathematica, Daniel Mansfield and N.J. Wildberger argue that Plimpton 322, the Old Babylonian tablets, served as an exact ratio-based trigonometric table.

… Instead, P322 is a trigonometric table of a completely unfamiliar kind and was ahead of its time by thousands of years.

… we must adopt two ideas that are unique to the mathematical culture of the Old Babylonian (OB) period, between the 19th and 16th centuries B.C.E.

First we abandon the notion of angle, and instead describe a right triangle in terms of the short side, long side and diagonal of a rectangle. Second we must adopt the OB number system and its emphasis on precision. The OB scribes used a richer sexagesimal (base 60) system which is more suitable for exact computation than our decimal system, and while they were not shy of approximation they had a preference for exact calculation. …

If this interpretation is correct, then P322 replaces Hipparchus’ ‘table of chords’ as the world’s oldest trigonometric table — but it is additionally unique because of its exact nature, which would make it the world’s only completely accurate trigonometric table. These insights expose an entirely new level of sophistication for OB mathematics.