Mathematicians Crack Mystery of Babylonian Clay Tablet 'Plimpton 322'

Australian scientists say the ancient Babylonians knew about a form of trigonometry far more advanced than the modern-day version. Discovered in the early 1900s, the tablet has been of interest to mathematicians for years because it describes Pythagoras' theorem, yet is thought to have been created around 1800BC, more than a thousand years before Pythagoras was born and started tinkering with triangles.

His "table of chords" on a circle is considered to be the oldest trigonometric table, but the Plimpton 322 tablet has knocked it off the top spot.

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

Dr Daniel Mansfield with the Plimpton 322 tablet.

The tablet isn't just a relic of a bygone era - to be confined to the recesses of the British Museum - either. He called it the world's oldest and the only completely accurate trigonometric table on record.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa sometime between 1822 and 1762 B.C., is now in the Rare Book and Manuscript Library at Columbia University in NY. (Glue residue found on the side suggest the break was recent.) The team used previous research on Plimpton 322 to speculate that it was originally built with six columns and 38 rows. The University of New South Wales Sydney researchers who cracked the code say the tablet was likely used by mathematical scribes to calculate angles when designing palaces, temples, step pyramids, and canals.

The UNSW Sydney, whose scientists discovered the goal 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.

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"It is a fascinating mathematical work that demonstrates undoubted genius", he said.

A key feature of Babylonian mathematics is that it used a clock-like sexagesimal number base of 60 rather than the decimal base-10 system.

But if the new study is right, then the Greek astronomer Hipparchus, who lived about 120 BC, is not the father of trigonometry that he's always been regarded as. "With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own", Dr. Wildberger said.

Mansfield and collaborator Norman Wildberger have published their findings in Historia Mathematica.

Said Daniel Mansfield: "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".

"The ancient Mesopotamians built largely out of clay and mud, so their structures didn't last that long", Wildberger said, adding that there were a few exceptions, "the most notable being the Ziggurat of Ur, which is still around - it was restored by later kings and also by Saddam Hussein - and dates from before the old Babylonian period".

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

(Copyright © 2015. All Rights Reserved.)
 
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