Geometric Dissections Now Swing and Twist
Greg N. Frederickson,
Professor of Computer Science
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, and form the other figure when swung another way. These dissections
have remained as magical as when the English puzzlist Henry Dudeney first
exhibited a hinged dissection of an equilateral triangle to a square
almost a century ago. Based on my recently published book,
Hinged Dissections: Swinging & Twisting, the talk will explore two fundamental ways to hinge
dissections of 2-dimensional figures such as regular polygons and stars.
The first way uses "swing hinges", which allow rotation in the plane.
The second way relies on "twist hinges", which allow
one piece to be turned over relative to another, using rotation
by 180 degrees through the third dimension. I will present
several techniques for designing both types of dissections
and demonstrate a variety of physical models.