And the Romans probably perfected it! Look at all those angles!

But of course, pi and other “circle stuff” would need to wait until scribes writing on paper with all those round letters.

Now being serious, I think that it’s possible that the Babylonians didn’t even discover it, but learned it from someone else. The Sumerians already used squares and rectangles extensively and had good maths, I wouldn’t be surprised if they tried to find a relationship between the distance of two opposite corners of a rectangle vs. the size of the sides of the rectangle, specially since this stuff has practical applications.