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== Title ==
Beyond Swinging: Hinged Dissections that Twist or Fold
== Speaker ==
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 ==
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.
Beyond Swinging: Hinged Dissections that Twist or Fold
== Speaker ==
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 ==
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.
