Happy October, Month of the Hexaflexagon! Oct. 21st is the annual Celebration of Mind, in honor of Martin Gardner. Maybe you'd like to host or attend a flexagon party sometime around then, or learn about other awesome Martin Gardnery things. Here's the official celebration website: http://www.puzzles.com/hexaflexagon/
For inspiration, here's pictures and stories from epic events in past years: http://www.puzzles.com/hexaflexagon/aroundtheworld.html
This video is based on, and in honor of, Martin Gardner's first Mathematical Games column from 1956, "Hexaflexagons," which can be found here: http://maa.org/pubs/focus/Gardner_Hexaflexagons12_1956.pdf
Historical Note: This video is based on a true story. Arthur H. Stone invented the Hexaflexagon and started a flexagon committee with his friends Tuckerman, Feynman, and Tukey (who all later became well-known in their respective fields). Tuckerman invented the Tuckerman Traverse, and Feynman invented Feynman Diagrams (not to be confused with Feynman Diagrams in physics, which is probably why flexagon diagrams are usually not called Feynman Diagrams anymore). The details of their interactions and dialogue, however, are my own invention.
-Feynman stuff is from the biography "Genius," by James Gleik, p. 103-104
-The story of how Gardner learned about flexagons is from "An interview with Martin Gardner" in the June/July 2005 Notices of the AMS, p. 602-611
-Other historical information, including the text and names on some of the letters, are from Gardner's original article: http://maa.org/pubs/focus/Gardner_Hexaflexagons12_1956.pdf
Thank you to the G4G-CoM committee for helping track down information, especially John Railing and Stan Isaacs for finding these sources.
Also check out flexagon.net, a pretty good resource for patterns for flexagons of many types, and of course the wikipedia page on flexagons: http://en.wikipedia.org/wiki/Flexagon
And on Martin Gardner: http://en.wikipedia.org/wiki/Martin_gardner