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© Copyright 2003, Jim Loy
Here is a triangle which I have approximated with some rectangles. As you distort the triangle by moving the red dot, each rectangle remains exactly the same (same size, shape, and area), it just moves left or right. It would seem that the area of the triangle remains the same, as long as the altitude remains the same. This is Cavalieri's principle, and can be applied to other plane figures (polygons and curved areas), and to volumes (cones, cylinders, pyramids, etc.). For example, it is a simple way to show that the volume of one cone (bent or leaning) is equal to that of a certain other cone (a right cone).
The above Java interactive demonstration was created with Cinderella (a geometry program).
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