Mathematical Tablet with Hexagon and Heptagon
Unknown · First Dynasty of Babylon, 1894-1595 BC
A square clay tablet twelve centimetres across carries geometry rather than accounts. On one face a hexagon is drawn; on the other a heptagon, a seven-sided figure, with the radius of its surrounding circle marked. The heptagon is divided into seven triangles, and inside one of them a cuneiform note explains how to work out its height. The inscription is badly damaged, but it seems to refer to the method used for both figures: calculating the height of a central triangle by applying a formula for the square root. The tablet is incomplete but the drawings are clearly legible.
Babylonian scribes worked in a base sixty number system and were remarkably skilled at approximations, including square roots, long before Greek geometry. This tablet shows that they also had a numerical theory of regular polygons. It was found at Susa, in the royal city district, in a batch of tablets buried under a large paving, and it came to the Louvre through the French excavations. Susa in this period used the Babylonian language and school curriculum, so the exercise could have been written in Babylon itself.
Did You Know? More than a thousand years before Euclid, a Babylonian scribe was calculating the height of triangles inside a seven-sided figure.
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