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Cavalieri’s Principle and 3D Printing

These 3D printed objects served as an excellent starting point for a classroom conversation on Cavalieri’s Principle.

3DP and Cavalieri

Each shape above is an extrusion of the same square.  In the middle, the square moves straight up; at left, the square travels in a complete circle from bottom to top; and at right, the square moves along a line segment and back.

The objects all have the same height.  Since at every level they have the same cross-sectional area, by Cavalieri’s Principle they all have the same volume!

Cavalieri’s Principle is a simple but powerful idea, and one that can be easily demonstrated around the house.  Here are some other examples using CDs and CD cases.



  1. James Fields says:

    Very cool! Any way you can link those .stl files so I can print them for class?

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