Cavalieri’s Principle and 3D Printing
These 3D printed objects served as an excellent starting point for a classroom conversation on Cavalieri’s Principle.
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.
3 Comments
Dan Meyer · May 26, 2015 at 11:20 am
WHAT’S A CD?!
MrHonner · May 26, 2015 at 3:12 pm
Excellent job anticipating student response.
James Fields · February 28, 2017 at 5:17 pm
Very cool! Any way you can link those .stl files so I can print them for class?