- Start Date:
June 25, 2009
- Event Start Time:
1:00 PM
- Event End Time:
2:00 PM
- Organizers:
Gene Fiorini
- Seminar Series:
REU Seminar
- Presenter(s):
Greg N. Frederickson - Purdue University
- Event Location:
DIMACS Seminar room
- Abstract:
A geometric dissection is a cutting of a geometric figure into pieces that can be rearranged to form another figure. Some dissections can be connected with hinges so that the pieces form one figure when swung one way on the hinges, and form the other figure when swung another way. In addition to using "swing hinges", which allow rotation in the plane, we can use "twist hinges", which allow one piece to be flipped over relative to another piece via rotation by 180 degrees through a third dimension, and also "piano hinges", which allow rotation along a shared edge, a motion that is akin to folding. We also employ piano hinges in a "stack-folding dissection", producing a single assemblage that represents a dissection of a figure that is p levels thick to a second figure that is q levels thick.
This talk will introduce a variety of twist-hinged, piano-hinged, and stack-folding dissections of regular polygons and stars, and also polyominoes. The emphasis will be on both appreciating and understanding these fascinating mathematical recreations. I will employ algorithmic and tessellation-based techniques, as well as symmetry and other geometric properties, to design the dissections. The goal will be to minimize the number of pieces, subject to the dissection being suitably hinged. Animations and video will be used to demonstrate the hinged dissections, in addition to actual physical models.
