**
**__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.

**inscribe****d 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
V_{i} V_{
j} is a motion whereby the section
of the polygon between V_{ i}
and V_{ j}
is rotated about the diagonal V_{ i}
V_{j}

*
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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