有趣的数学问题-两个圆的重叠

问题陈述

问题的实质

找到两个圆相交的重叠区域。

The whole picture shown in the blow:

The matlab plot code:

The way to solving this problem :Part I

Rotate the figure 2 and draw the subline to help us to solve this question, then we will get:

Starting from the top left, clockwise, define the four triangles and fan-shaped as t1, t2, t3, t4 and f1, f2, f3, f4.

Then, the overlap area will be:

which can be convert as:

Bring this method back to the origin plot, we can get

Calculate the VIP: Part II

First, we need write the two different circle function:

and

Calculate the cross point,

Calculate the overlap area: Part III

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