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February 06, 2018 Tuesday 09:46:28 AM IST

Babylonian Clay Tablet Resonates well with the Indian Mathematical Wisdom

Science Innovations

The library of Columbia University in New York possesses a 3,700-year- old Babylonian tablet called Plimpton 322, which has defied any attempts of interpretations so far. P322, the small clay tablet was discovered in the early 1900s by Edgar Banks in today’s southern Iraq. Scientists of the University of New South Wales have recently deciphered P322 and have brought out amazing revelations about the clay tablet.

The new results suggest that the Babylonians beat the Greeks to the invention of trigonometry, the study of triangles, by much more than 1,000 years. The researchers identified P322 as one of the world's oldest and most accurate trigonometric table, much older than that developed by the star mathematician of India, who lived in the Sangamagrama in Kerala, near the southern tip of India, who founded the famous Kerala School of Astronomy and Mathematics in the late 14th Century. Babylonians might have found use for trigonometry in the architectural calculations of palaces, temples or canals, it is assumed.

Written in the cuneiform script, the Plimpton 322 makes use of a unique number system which uses a base 60 or so called sexagesimal system, written using four columns and 15 rows of numbers.

“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles. It is a fascinating mathematical work that demonstrates undoubted genius,” says Professor Norman Wildberger, who has published the results in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.

The researchers have found that the contents of P322 matches well with the well-known sine table created by the Indian astronomer-mathematician Madhava (1340–1425 CE) from Kerala. Madhava is believed to have created his table using the power series expansion.

The researchers also believe that P322 is superior to the Madhava’s tables on three counts. The first and simplest reason is that P322 contains 38 rows compared to the 24 rows in Madhava’s table. Secondly Madhava’s table concentrates on values of sin, which are useful but limited. While, the holistic approach of P322(CR) gives you the entire triangle. Thirdly, the completely correct aspect of P322(CR) means that numerical calculations are more precise.

It turns out that for sophisticated applications of trigonometry, the exact sexagesimal trigonometry is both more general and powerful, with the laws of rational trigonometry being polynomial, typically of degree two or three.

The discovery of trigonometry is traditionally attributed to the ancient Greeks, which awaits a revisit on the basis of the new revelations. The Babylonians had much earlier, computationally simpler and more precise style of exact sexagesimal trigonometry! This different and simpler way of thinking, in fact, has the potential to unlock improvements in science, engineering, and mathematics education today.