Ancient Babylonians Do It Again!

Babylon – in ancient Mesopotamia, now Iraq – hosted one of the earliest recorded civilisations. Partly because they became a trading nation, they developed some of the earliest mathematical techniques. We already know that they were aware of what we now call Pythagoras’ Theorem (in a numeric sense, since algebra didn’t exist), but the some of the secrets of a tablet known as Plimpton 322 have been unravelled to show that they had developed a highly sophisticated form of trigonometry, some 1000 years before its supposed invention by the Greeks.

Mathematical table. Replica of a Babylonian Clay Tablet – Plimpton 322. MA.315226.

How could trigonometry be useful to an early civilisation? Possibly because they needed to be able to do accurate calculations for building their palaces and pyramids. Of course, they didn’t invent concepts such as the sine and cosine of angles, but the tablet appears to contain trigonometrical tables for angles from near horizontal to near vertical. And all this may be connected to the fact that their numbers were based on the sexagesimal, or base 60, system, unlike our decimal system. 10 can only be divided into halves and fifths, whereas 60 can be divided into many different parts – importantly, it can be divided by 2, 3, 4, 5 and 6, thus making it easier to draw up tables of calculation entirely using whole numbers.

Earlier research had dismissed the possibility that the table of numbers represented trigonometric ratios, but an Australian academic has claimed that the tablet displays a novel type of trigonometry. Dr Mansfield says that ‘it is a fascinating mathematical work that displays undoubted genius.’ Professor Norman Wildberger, who worked with Dr Mansfield, said: ‘It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.’

(Image: Smithsonian Institute)

A couple of my earlier blogs relate to material in this one. See here for a proof of Pythagoras’ Theorem; and here for some comments on ‘imperial’ units of measurement.

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