Aug 28, 2017

Babylonians may have done trigonometry 1000 years before the Greeks

UNSW/Andrew Kelly

A team of mathematicians studying a famous Babylonian tablet have come to a startling conclusion: the ancient people who created the tablet had an in-depth knowledge of trigonometry, and used a method that is in some ways more accurate than our own. The research was published in the journal Historia Mathematica.

Why it matters: The tablet, which predates Greek trigonometry by about 1000 years, shows a radically different approach to math. "We have to really get outside of our own culture to see from their perspective to be able to understand it," Daniel Mansfield, the paper's lead author, told Science.

The tablet, Plimpton 322, was discovered in the 1920s by J. Edgar Banks, who served as the inspiration for Indiana Jones. Researchers have known for years that the tablet depicts a chart of triangle side measurements that follow Pythagorean ratios (think a2 + b2 = c2), but no one knew why the Babylonians decided to record those numbers, reports Ron Cowen for Science.

How it works: Modern trigonometry is based on approximations, in part because our mathematics is a base-10 system. This means our math requires lots of decimal points or rounding, like when you divide 1 by 3. But the Babylonians used a system based around 60s, like a modern clock. It made division easier for them, just like we can easily divide an hour by 1, 5, 10, 12 and others without using decimals.

What it means: This math system let them describe triangles using a precise ratio of sides. The researchers think it could have been used in construction, allowing them to use the size of a pyramid base and the height of a pyramid to calculate the length of the sloped portion.

Not so fast: Although exciting, this interpretation of the iconic tablet isn't set in stone. Half of the relic is missing — the half researchers speculate has the solutions to the trigonometry problems and would help determine if this tablet isn't just a list of Pythagorean triangles, but an actual tool that uses a novel kind of trigonometry to calculate them.

"Apart from the column headings, the tablet just consists of columns of numbers, and this invites a great deal of purely mathematical speculation," Duncan Melville, who studies Mesopotamian mathematics, told National Geographic.

Go deeper: Watch this video, produced by University New South Whales in Australia, to see the tablet and read this article The Conversation by the authors of the paper.

Go deeper