Trapezoids are, oddly enough, fundamental to modern science. When European scientists used them to simplify certain astronomical calculations in the 14th century, it was an important first step toward calculus—the mathematics Isaac Newton and Gottfried Leibniz developed to understand the physics of astronomical objects like planets. In other words, trapezoids are important, and we’ve known this for nearly 700 years.

Well, the Babylonians knew all of that 14 centuries earlier, according to new research published in *Science*, proving once again that ancient societies were way more advanced than we’d like to think.

To understand why trapezoids are important to mathematics, consider this basic question: If a car is moving at 30 miles per hour, how far will the car have traveled after, say, a minute? Easy: Thirty mph times one minute (or one-sixtieth of an hour) equals half a mile. You can represent this solution geometrically as the area of a rectangle. One side corresponds to the speed of the car (30 mph), and the other to the amount of time that’s past (one minute), while the area is the distance traveled.

### Ancient societies were way more advanced than we’d like to think.

Without going into technical detail, it turns out trapezoids can help you solve a more difficult version of this problem where the car is accelerating at a constant rate—say, starting out at 15 mph and increasing speed by one mile per hour every two seconds until you reach 45 mph. European mathematicians, including the Oxford Calculators and Nicole Oresme, figured that out by the middle of the 14th century, and historians thought that was as far back as the ideas went.

But, according to researcher Mathieu Ossendrijver, there’s evidence the Babylonians had reached the same conclusions much earlier. An astrophysicist-turned-historian of ancient science at Humboldt University in Berlin, Ossendrijver bases his conclusion on a re-analysis of four Babylonian tablets, all dated to the first century B.C.E. or earlier, and a fifth one recently re-discovered in the British Museum’s archives.

The first four tablets contain a mathematical computation (in cuneiform, using a base-60 number system) of the area of a trapezoid, but few references to astronomy aside from a mention of the planet Jupiter, some speeds, and some lengths of time. The fifth contains the complete calculation, but without any indication of what it means—no mention of Jupiter, trapezoids, or any of that. The last piece of the puzzle comes from a few other tablets that show incomplete calculations, but more specific references to Jupiter and astronomical numbers.

Taken together, the picture becomes clear: Babylonians, Ossendrijver argues, used trapezoids to guide their calculations of Jupiter’s motion across the sky. More broadly, they had made a series of abstractions to understand the real, physical world, and they’d done it long, long before a bunch of English and French guys—our mathematical ancestors—managed it.

Leave it to the Babylonians to remind us of our place in the universe.

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