Cavalieri’s Principle

Even though I don’t mince words when I proclaim my dislike of geometry, there are times when its simplicity and elegance strike me. Today the geometry teacher at my school was talking about Cavalieri’s Principle. Coincidentally, in my 7th grade math class, we are learning about volumes of prisms, cones, pyramids, and maybe spheres.

It got me thinking: without calculus, where do we get the formula for spheres? I mean, with calculus, it’s cake, but let’s assume we don’t have calculus.

These two things in mind led me to this great blog post on Cavalieri. It’s pretty much a proof without words, so I’m going to crib the picture from the post,

but the post has words explaining the picture. So click on the link and check it out if you are still scratching your head.