Ancient Babylonian trigonometry? Really? Really???

It’s pretty clear what this clay tablet says, right? Obviously it’s written in…

Oh, wait, maybe it isn’t so obvious.

You probably don’t read Babylonian, or Akkadian, or Sumerian, or whatever language these cuneiform carvings represent. But this tablet has surprisingly been in the news a lot recently. “Some researchers say the Babylonians invented trigonometry — and did it better,” claims an article in Popular Science.

But don’t believe everything you read, as I like to tell my students. “Don’t Fall for Babylonian Trigonometry Hype,” warns a headline in Scientific American. As the accompanying article points out, this tablet has long been well known in certain circles, especially among those of us who have studied both history of math and ancient cultures:

The far right column consists of the numbers 1 through 15, so it’s just an enumeration. The two middle columns of Plimpton 322 contain one side and the hypotenuse of a Pythagorean triangle, or a and c in the equation a2+b2=c2. (Note that a and b are interchangeable.) But these are a little brawnier than the Pythagorean triples you learn in school. The first entries are 119 and 169, corresponding to the Pythagorean triple 1192+1202=1692. The far left column is a ratio of squares of the sides of the triangles. Exactly which sides depends slightly on what is contained in the missing shard from the left side of the artifact, but it doesn’t make a huge difference. It’s either the square of the hypotenuse divided by the square of the remaining leg or the square of one leg divided by the square of the other leg. In modern mathematical jargon, these are squares of either the tangent or the secant of an angle in the triangle.

The trouble is that we know what the table in the tablet is, but not how it was used. Any speculation that it was a trig table is just that: speculation. Even the august New York Times has fallen for the hype. You can check out these links, or read the summary at Math With Bad Drawings.


Categories: Math