patrick honner

After demonstrating Cavalieri’s Principle with empty CD cases, I thought I’d do the same with the actual CDs.

Here we see a bunch of discs stacked up to make a right cylinder.

To compute the volume of this cylinder, it would be sufficient to know (a) the volume of one CD, and (b) the number of CDs in the stack.  We would simply multiply the two together to get the volume.

The argument is less obvious, but essentially the same, regardless of how the CDs are stacked!  So this “prism”

has the same volume as  the original cylinder.  Now, this object should also have the same volume

however some center-of-mass issues may foil our elegant mathematical demonstration.

Related Posts

• CDs and Cavalieri’s Principle
• CDs, Prisms, and Parallelepipeds
• CD Packing Problems

More from my fun with folding series:  after having fun making paper pyramids, I thought I’d try out foam board as a medium.  As before, I began by connecting the midpoints of the sides of the triangle to form its medial triangle.

Then I scored the medial lines, bent, and taped!

A rotation gives a sense of how oblique this pyramid is.

My students and I enjoy exploring questions like “Will this procedure always produce a pyramid?” and “What other kinds of solids can be formed in this manner?”

Related Posts

• Fun With Folding
• Paper Pyramids
• Triangular Tables