Hexaflexagons are gadgets invented by the topologist Arthur H. Stone and popularized in Martin Gardner's Scientific American Column. The article appears in his book Mathematical Puzzles and Diversions.
This presentation is more of a workshop than a talk. First, we construct hexaflexagons with three faces and with six faces and learn how to flex them. In playing with the hexahexaflexagon, novices are quickly struck by the difficulty of locating all six faces. We then have a discussion of how to resolve this problem, and if a solution is reached, we discuss how to construct hexaflexagons with different numbers of faces and different internal structures.
You need to be able to write numbers, to crease a sheet of paper along a marked line, to apply adhesive, and to follow instructions. That's it.
If the audience has higher mathematical capability, we cover more ground accordingly.
I use an overhead projector and, if available, a blackboard. I supply the paper strips for folding and ask that the audience bring pencils. I also bring glue and tape, but local sources of more glue and/or tape help speed the flexagon assembly process.
Printed Flier for Radical Pi Talk