Science

Babylonians developed trigonometry 3700 years back, much earlier than Greeks

Babylonians developed trigonometry 3700 years back, much earlier than Greeks”

"The huge mystery, until now, was its goal - why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet", Mansfield said.

Australian scientists say the ancient Babylonians knew about a form of trigonometry far more advanced than the modern-day version.

He wrote the paper with UNSW Associate Professor Norman Wildberger.

Plimpton 322 was discovered in the early 1900s in southern Iraq by Edgar Banks, an archaeologist who the fictional character Indiana Jones was based on, the scientists said.

For decades mathematicians have puzzled over the four columns and 15 rows of numbers written on this particular tablet in its cuneiform script.

'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'. "Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids", said Mansfield, who first read about the tablet when preparing material for first-year math students.

After conducting a historiographical analysis of the tablet's purported goal, Mansfield and Wildberger took a closer look at the tablet and its inscriptions.

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Its use of ratio-based trigonometry rather than trigonometry based on angles and circles makes it the world's most accurate trigonometric table, Dr Mansfield says. It opens up new possibilities not just for modern mathematics research, but also for mathematics education.

Allen noted the most important finding from the tablet is the evidence of Pythagorean triples, indicating that Babylonians were seemingly aware of the Pythagorean theorem-years before Pythagoras.

Traditionally, Greek astronomer Hipparchus is credited with inventing trigonometry around 120 B.C. However, this tablet predates the astronomer by over 1,000 years. If the UNSW study does show how the tablet was used to find approximate solutions to equations involving triangles, only speculative historical context can determine exactly how the tablet was applied in day-to-day life said Wildberger. Its 15 rows describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

Building on previous research, Mansfield and Wildberger were able to show that two columns and 23 rows are missing-the original tablet contained six columns and 38 rows. In the study, the authors used the ancient base 60 system to demonstrate how scribes would have arrived at the numbers that were chiseled on Plimpton 322. Dr Daniel Mansfield of the School of Mathematics and Statistics at UNSW attested to this benefit.

The ancient Babylonians had an advantage over our current counting system because they use base-60, instead of the base-10 system that we use.

"This is a rare example of the ancient world teaching us something new".



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