Prismplay

This month's column deals with volumes of prisms and regular antiprisms and was inspired by some interesting results I found in Blackwell's Geometry and Architecture. I highly recommend this book to anyone who teaches geometry because it contains a wealth of interesting applications of what is currently taught in a plane geometry course.

What caught my eye were some results about prisms that could be used as a nice supplement to material that appears in many current geometry textbooks. The results have to do with the total surface area of a prism and its exposed surface area, which is the area of the sides plus the area of the top.The latter is of architectural interest because if you were building a structure in the shape of a prism, the base would not be exposed to the elements.

The former makes sense if you were thinking of an interior space such as a room. In what follows, remember that a regular prism is one in which all the edges are equal and all the lateral faces are squares. Here is what Blackwell has to say about which of the regular prisms is the most efficient in the sense that for a given volume the surface area is a minimum.