A geometry and algebra thread – Constructing, and using, Jennifer's puzzle
Peter Hilton, Jean J. Pedersen, Sylvie Donmoyer · Cambridge University Press eBooks · 2010
Required materials Strips of paper (preferably of different colors) Heavy paper, such as lightweight cardboard Paper clips Optional materials Ruler Compass Facts of life In many instances involving the use of geometry in the real world, we need to make adjustments to take into account the realities of life . For example, paper comes in various thicknesses (which are never zero!) and the interior of every container must be larger than what it contains. These and other very elementary facts of reality affect how we are able to take practical advantage of the theorems obtained from our study of the geometry of idealized lines, planes, and solids. As this section title implies, we concern ourselves here with the details of practical construction , in this case of a particular set of nested polyhedra. Namely, we construct an octahedron and 4 tetrahedra that fit inside a larger tetrahedron that, in turn, fits inside a cube. As you will see – assuming that you become actively involved in carrying out these instructions – overcoming the difficulties encountered in using, in a real-life situation, a theory that is perfect in principle is very much a skill of the eyes and hands as well as of the mind. What follows is first a description of the construction, along with some hints about how to solve Jennifer's puzzle; this is followed by some important mathematical consequences to be gained by constructing the puzzle.