Forget Pythagoras! The Babylonians Knew Their Trigonometry Before the Greeks

Plimpton 322

Forget Pythagoras! The Babylonians Knew Their Trigonometry Before the Greeks

Researchers at the University of New South Wales in Sydney, Australia say they have discovered just that by studying the objective of a famous 3,700-year old Babylonian clay tablet called Plimpton 322, which they believe is actually the world's oldest and most accurate trigonometric table.

But what if Hipparchus' table wasn't the first and another ancient civilization was using tablets to calculate geometric problems long before the Greeks?

Discovered by 20th century archaeologist Edgar Banks, the ancient clay fragment, known as Plimpton 322, has puzzled scientists for decades.

Relationships between numbers in the completed table would have represented a novel type of trigonometry - one that relied on ratios instead of angles and circles, according to the study. Experts believe the tablet would most likely have been used by ancient architects to construct buildings in Babylonia. It has four columns and 15 rows of number in modern cuneiform script written in a base 60, or sexagesimal, system, Newsweek reports. Sixty being, of course, far easier to divide by three. Also, the left-hand edge of the tablet is broken, meaning parts of Plimpton 322 are missing.

He added: "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".

The tablet isn't just a relic of a bygone era - to be confined to the recesses of the British Museum - either. (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. "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.

Hipparchus - the Greek astronomer, who lived in about 120 BC - was always been regarded as the father of trigonometry.

Professor Norman Wildberger, who worked with Mansfeld on the research, also believes there is a lot more to discover from the ancient inhabitants of Iraq. "It is a fascinating mathematical work that demonstrates undoubted genius", Dr. Mansfield said.

Generations of schoolchildren have learned that Ancient Greek thinkers invented trigonometry - but rows of numbers deciphered on an ancient stone tablet have turned that idea upside down.

"Apart from the column headings, the tablet just consists of columns of numbers, and this invites a great deal of purely mathematical speculation", said Melville in an emailed statement to National Geographic. "With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own".

Mansfield read about Plimpton 322 by chance and made a decision to study Babylonian mathematics after realising that it had parallels with the rational trigonometry of Wildberger's book Divine Proportions: Rational Trigonometry to Universal Geometry.

"It's rare that the ancient world teaches us something new".

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