COSAM » Events » 2018 » January » DMS Topology Seminar

DMS Topology Seminar |

Time: Jan 31, 2018 (02:00 PM) |

Location: Parker Hall 246 |

Details: Speaker: Title: Inverse Limits of Flexagons Abstract: Flexagons were first introduced in 1939 by Arthur H. Stone when he was a graduate student at Princeton, and they were popularized by Martin Gardner in the December 1956 issue of Mathematical studies of flexagons have concentrated on the combinatorial properties of flexagons created with a finite number of polygons. Here, we consider an infinite version which can be created either using inverse limits or nested intersections of solid tori (viewed as a folded annulus cross the unit interval). If $n \ge 3$, then a strip of $3n$ equilateral triangles can be folded into a hexaflexagon which (after the ends are identified) is topologically an annulus if $n$ is even and a Möbius strip if $n$ is odd. Of these, the most natural ones are created using $9(2^n)$ triangles, leading to the construction of a space (via either inverse limits or nested intersections) which (viewed as a subset of $\mathbb{R}^3$ in a natural way) mimics the properties of all of the hexaflexagons having finitely many triangles. Some preliminary results on the properties of this space will be discussed.
(Paper toys will be provided to the audience as visual aids.) |