Definitions

angle-monotone motion :a motion in which each vertex angle is a monotone function in time.

configuration: a polygon with the same counterclockwise set of edge lengths as another.

convexify : to reconfigure a polygon into a convex one.

convex configuration:   a convex configuration of edge lengths L 1 , L 2 , ..., L n  is a convex polygon with edge lengths in that counterclockwise order.

distance-monotone motion : a motion between two convex polygons in which every distance between a pair of vertices varies monotically with time.

hyperplane-flip:  similar to a pivot, a hyperplane-flip of a polygon P consists of the reflection of a polygonal chain of P across a hyperplane H supporting the convex hull of P and containing at least two vertices of P.

inscribed configuration: a configuration in which each of the vertices of a polygon are co-circular.

linkage: a closed set of hinges and rigid bars; the hinges can be seen as "linking" the bars together, and allowing the bars motion limited only by their dinmensional  space and their attachment to another link.

motion : see reconfiguration

pivot: a pivot on line segment Vi V j is a motion whereby the section of the polygon between V i and V j is rotated about the diagonal V i Vj

polygon:   here polygon P is characterized by
• its vertices, denoted V 1, V 2, ..., V n in counterclockwise order.
• its edges E i, where E i = (V i, V i+1)
• its edge lengths l  = | E i| = | V i V i+1|
All operations carried out on polygons of n vertices will be done modulo n.

reconfiguration: a continuous function of time from the unit interval [0,1] to a configuration.

universality: the proving of a number of variations of a result by numerous independent sources, leading to the acceptance that result is generalizable to many cases (or universal).

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