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What mathematical history do circles and sectors involve?
From the origin of mathematics, mathematics in ancient Egypt and Mesopotamia was the earliest, but mathematics in China and India was the last.

In the existing papyrus, there are formulas about various graphic areas, in which the circular area is approximate. In the 50 th question of Rhine papyrus, it is mentioned that the area of a circle is approximately square, but there is no clear proof.

One of the three major geometric problems in ancient Greece: turning a circle into a square, that is, making a square with the same area as a given circle.

Anna Golas first studied the method of turning a circle into a square, and then An Dengfeng, a representative of sophistry school, first proposed the method of approximating the circle inscribed by a regular polygon. This is the "exhaustive method" in ancient Greece. The circle area of Fang Zhangtian's formula of "Rounding Field" in China's Nine Chapters Arithmetic. There are many others that I won't list one by one.