3,700-year-old Babylonian tablet ‘decoded’, revealing true birth of trigonometry



Mathematicians everywhere will be thrilled by the solving of this 3,700-year-old tablet, which experts at the University of New South Wales, Australia (UNSW), have discovered to be the world’s oldest trigonometric table but further complex. 
Almost a century ago, Edgar Banks – dug up a clay tablet in southern Iraq and sold to a collector George Plimpton in 1945 for $10 (£8), its fate was far from sealed, and it’s confounded mathematicians ever since, but it took until now for it to make sense. With this explanation has come insight into Babylonian mathematics which in some ways preferable, system than our own.



The tablet’s accuracy is pretty much unparalleled, due to the Babylonian way of approaching arithmetic; Babylonian maths uses a base of 60 – a sexagesimal system, as opposed to the 10 used in modern mathematics. Sixty being far easier to divide by three. Which means that the calculations are generally more accurate. Dr Daniel Mansfield of the School of Mathematics and Statistics at UNSW attested to this benefit. “The tablet not only contains the world’s oldest trigonometric table,” he said, “it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.”

Surprisingly The idea of Plimpton 322 (The Babylonian tablet) as a trigonometric table had been raised before, and eventually rejected, but this was done in the absence of an understanding of Wildberger's methods.


Mansfield and Wildberger concluded that the ancient Babylonians had beaten Wildberger to his ideas by almost four millenia now, albeit only for right-angled triangles. They report in Historica Mathematica that instead of using sinΘ, cosΘ, and tanΘ as we do – something we of course inherited from the ancient Greeks – Plimpton 322 could be used by anyone needing to know the length of one side of a right-angled triangle by finding the closest match to the two known sides.

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