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

Mathematicians everywhere will be enthralled by the recent decoding 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. Lovers of Ancient Greece, in the meantime, will be dismayed to realise that trigonometry, hitherto attributed to the Greeks, actually emerged 1,500 years prior to their society, in Babylonia.

The clay tablet which started it all (now there’s a sentence you never thought you’d read) is known as Plimpton 332, was uncovered by explorer Edgar Banks in southern Iraq almost 100 years ago. Sold to collector George Plimpton in 1945 for $10 (£8), its fate was far from sealed, and it’s confounded mathematicians ever since…

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Until now. The tablet, it has been discovered, proffers the world’s oldest trigonometric table, describing the shape of right-angle triangles based on ratios, as opposed to angles and circles, which is the conventional method. Experts believe the tablet would most likely have been used by ancient architects to construct buildings in Babylonia.

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, for those in the know – as opposed to the 10 used in modern mathematics. Sixty being, of course, 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.”

The tablet isn’t just a relic of a bygone era – to be confined to the recesses of the British Museum – either. Whilst, Dr Mansfield relays with more than a hint of dismay, “Babylonian mathematics may have been out of fashion for more than 3000 years”, the trigonometric table in question could have applications in modern industries like surveying, education, and computer graphics.

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