Ancient Baylonians Rocked Trigonometry

Recently an ancient Babylonian tablet was finally deciphered after almost a century of study. Researchers from the University of New South Wales discovered that the tablet, known as Plimpton 322, appears to be a set of trigonometric tables that are more accurate than those currently in use. This is because the Babylonians used base-60 calculations, which unlike base-10 is evenly divisible by 3.

Mathematicians have been arguing for most of a century about the interpretation of the tablet known as Plimpton 322, ever since the New York publisher George Plimpton bequeathed it to Columbia University in the 1930s as part of a major collection. He bought it from Edgar Banks, a diplomat, antiquities dealer and flamboyant amateur archaeologist said to have inspired the character of Indiana Jones – his feats included climbing Mount Ararat in an unsuccessful attempt to find Noah’s Ark – who had excavated it in southern Iraq in the early 20th century.

Mansfield, who has published his research with his colleague Norman Wildberger in the journal Historia Mathematica, says that while mathematicians understood for decades that the tablet demonstrates that the theorem long predated Pythagoras, there had been no agreement about the intended use of the tablet.

“The huge mystery, until now, was its purpose – why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet. 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. It is a fascinating mathematical work that demonstrates undoubted genius.

“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. This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3,000 years, but it has possible practical applications in surveying, computer graphics and education. This is a rare example of the ancient world teaching us something new.”

A number of people have objected to that last bit, because we actually have picked up a lot more technological ideas from the ancient world than most people generally recognize. For example, back in the 1970's there was all this speculation about how aliens must have cut the stones found in various Egyptian monuments because the tool marks showed speeds that would destroy the most modern saws of that time. But then, somebody figured out the trick.

Egyptian saws used large circular blades so that the edge could move extremely fast relative to the stone. They then ran the blade through a pool of water as it spun to cool it - and presto, super-fast tool marks. If you have a granite countertop today it was probably cut with an ancient Egypt-inspired water saw. The ancients were just as smart as we are, they just were operating from a completely different baseline technology.

Prejudice against the ancient world aside, though, this is a highly significant discovery that demonstrates the sophistication of Babylonian mathematics. It's no wonder that they were famed architects and engineers of the ancient world.