Ancient tablet offers new angle on the birth of maths
Artefact found by real-life Indiana Jones shows Babylonians discovered trigonometry, not Greeks
A 3,700-YEAR-OLD clay tablet has proved that the Babylonians developed trigonometry 1,500 years before the Greeks and were using a sophisticated method of mathematics that could change how we calculate today. The tablet, known as Plimpton 332, was discovered in the early 1900s in southern Iraq by Edgar Banks, an American archaeologist and diplomat, who was the inspiration for the Indiana Jones films.
The true meaning of the tablet has eluded experts until now but research by the University of New South Wales, Australia, has shown it is the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, palaces and canals.
“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
‘It has great relevance. This is a rare example of the ancient world teaching us something new’
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.”
Hipparchus, a Greek astronomer who died in around 120BC, 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 right-angled triangle using just one known ratio.
The tablet, thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822BC and 1762BC. It is now in the Rare Book and Manuscript Library at Columbia University in New York.
“Plimpton 322 predates Hipparchus by more than 1,000 years,” says Dr Wildberger. “It opens up new possibilities not just for modern mathematics research, but also for mathematics education.
“A treasure trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us.”
The study is published in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.