Babylonian mystery solved: 3700-year-old 'Indiana Jones' tablet reveals its secrets

Plimpton 322

It has four columns and 15 rows of numbers written in cuneiform script.

The Greek astronomer Hipparchus, who lived about 120 BC, is broadly considered "the father of trigonometry" for compiling the first known "table of chords" or trigonometric table, which allows users to figure out the ratio of two sides of a right-angle triangle with only one known ratio. 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.

Australian scientists have managed to crack the code of a mysterious 3,700-year-old Babylonian clay tablet, revealing a level of mathematical sophistication that pre-dates the ancient Greeks by a whopping 1,500 years.

"We also demonstrate how the ancient scribes, who used a base 60 numerical arithmetic similar to our time clock, rather than the base 10 number system we use, could have generated the numbers on the tablet using their mathematical techniques". The tablet is now kept in the Rare Book and Manuscript Library at Columbia University in NY.

What's more, because of the way the Babylonians did their maths and geometry, it's the most accurate trigonometric table as well as the oldest. "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".

"Bottom line is this", says Allen, "if interpreted as a trig table, it would be the oldest known".

"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".

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An ancient Babylonian tablet discovered in the early 1900s has always been a puzzle to scientists.

You can see Plimpton 322 itself here, where you will also learn that commercial reproduction of images depicting the tablet is forbidden without permission. The study authors expanded on prior research suggesting that Plimpton 322 was broken and incomplete, and they determined that there were originally six columns of figures on the tablet.

This study's findings hint that these understudied artifacts from a long-dead empire could hold exciting discoveries, not only for understanding the history of mathematics but also for enhancing how math is studied today, Wildberger explained. "It is a fascinating mathematical work that demonstrates undoubted genius", he said in the paper published in the journal Historia Mathematica.

NSW researchers Dr Daniel Mansfield and professor Norman Wildberger say the identification of a pattern called "Pythagorean triples" was a key clue to pinpointing the tablet's objective.

The UNSW Sydney, whose scientists discovered the objective of the tablet, said the left-hand edge of the tablet is broken and the researchers build on previous research to present new mathematical evidence that there were originally six columns and that the tablet was meant to be completed with 38 rows.

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

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