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Hipparchus, a Greek astronomer who died around 120 BC, has long been regarded as the father of trigonometry, with his “table of chords” on a circle considered the oldest trigonometric table. Such tables allow a user to determine two unknown ratios of a rightangled triangle using just one known ratio.
However, a 3,700-year-old clay tablet has recently proved that the Babylonians developed trigonometry more than 1,500 years before the Greeks and were using a sophisticated method of mathematics that could change the way we calculate today. The tablet, known as Plimpton 332, was discovered early last century in the ancient Sumerian city of Larsa in southern Iraq by Edgar J Banks, an American archæologist and diplomat, said to be the inspiration for the
Indiana Jones films. Dated by its cuneiform style to between 1822 BC and 1762 BC, the tablet was bought from Banks by the New York publisher George Arthur Plimpton who bequeathed it with the rest of his collection to Columbia University, New York, in the 1930s.
The partly broken tablet measures 13 by 9cm (5x3.5in), and is 2cm (0.78in) thick. Scholars at the University of New South Wales in Sydney have now shown that the four columns and 15 rows of cuneiform script constitute the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, pyramids, palaces and canals. The base 60 employed in calculations by the Babylonians permitted many more accurate fractions than our base 10.
“Our research reveals that Plimpton 322 describes the shapes of right-angled triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Daniel Mansfield of the School of Mathematics and Statistics at the UNSW Faculty of Science. “It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry. This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3,000 years, but it has possible practical applications in surveying, computer graphics and education. This is a rare example of the ancient world teaching us something new.” D.Telegraph, Guardian, 25 Aug 2017.