Flexagons
Flexagons are a fascinating collection of mathematical "toys" made from folded strips of paper and having complex properties beyond what one might originally suspect from such humble materials. As highschool students, my close buddy, Tony Conrad, and I were introduced to these objects by Harold V. McIntosh, a mathematician then working at Aberdeen Proving Ground and then at the Research Institute for Advanced Study (RIAS), an affiliate of the Martin Company, in Baltimore. "Mc" (pronoundced "Mac") became our good friend and mentor, feeding our interest in many areas of mathematics, epecially group theory, which was his specialty. The summer of our graduation (1957), he subsidized a research project for Tony and me to study flexagons, leading to a couple of papers on the subject published as RIAS Technical Reports. Included is the magnus opus posted here. Mc's account of this time gives some fascinating flexagon history. At least as important for me, he persuaded RIAS to sponsor a summer course on computer programming at Morgan State College in 1961, which he taught. We learned IBM 709 assembly language, and LISP. My LISP project was to write a program to "flex" a flexagon, properly keeping track of its pat structure. It was my introduction to the world of computers that has been central to my work ever since. I owe a lot to this early start.
Martin Gardiner deserves the primary credit for the original publicizing of flexagons (he called them "hexaflexagons," as many still do) in two articles in his famous column in Scientific American. Flexagons are everywhere on the Web these days. Google does a better job than ever I could at pointing to relevant pages. However, "Mc" (now at the Universidad de Puebla in Mexico) has returned to the study of flexagons in recent years, and I particularly recommend his web postings on the subject.
For a pattern for making a simple 6-faced "hexaflexagon" click here.
Selected mirror documents:
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