A、To explain how angles are measured. B、To prove that Mesopotamiansdid not know how to use square numbers. C、To discuss a mistak

Let me warn you against a mistake that historians of science often make. They sometimes assume that people in the past use the same concepts we do. Here is a wonderful example that makes the use of history of mathematics some while ago. It concerns an ancient Mesopotamian(美索不达米亚人) tablet that has some calculations on it using square numbers. The calculations look an awful one like the calculations of the link of the sides of triangle. So that’s what many historians assume they were. But using square numbers to do this is a very sophisticated technique. If the Mesopotamians knew how to do it, as historians started thinking that they did. Well, they learn math with incredibly advanced. Well, it turns out the idea of Mesopotamians use square numbers to calculate the link of triangle’s sides is probably wrong. Why? Because we discovered that Mesopotamians didn’t know how to measure angles, which is a crucial element in the whole process of triangle calculations. Apparently the Mesopotamians had a number of other uses for square numbers. These other uses were important but they were not used with triangles. And so these tablets in all likelihood were practice sheets, if you like, for doing simpler math exercises with square numbers. In all likelihood, it was the ancient Greeks who first calculate the link of triangle’s sides using square numbers. And this was hundreds of years after the Mesopotamians.