CATS-Sep-24-2012
Title[edit]
Beyond Swinging: Geometric Dissections that Swing or Twist
Speaker[edit]
Greg N. Frederickson received a Ph.D. in Computer Science from the University of Maryland in 1977. He is now a Professor of Computer Science at Purdue University, in West Lafayette, Indiana, with his primary area of research in the design and analysis of algorithms. He has served on the editorial boards of SIAM Journal on Computing, SIAM Journal on Discrete Mathematics, Algorithmica, and IEEE Transactions on Computers. He also pursues interests in mathematical recreations, specifically geometric dissection. On this topic he has published three books and a number of articles. He has twice won the George Polya Award from the Mathematical Association of America.
Abstract[edit]
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. Furthermore, we can use "fold hinges", which allow rotation along a shared edge, a motion that is akin to folding.
This talk will introduce a variety of twist-hinged and fold-hinged dissections of regular polygons and stars, and other figures such as 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.
