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3
votes
1answer
267 views

A.J. Galitzer's Ph.D. thesis: On the moduli space of closed polygonal linkages on the 2-sphere

Recently I became curious about moduli spaces of linkages and so I found and began reading some papers of Kapovich and Millson. In the paper Hodge theory and the art of paper folding, the Ph.D. ...
6
votes
2answers
301 views

Calabi-Yau manifolds and polygonal linkage configuration spaces: related?

I was reading about Calabi-Yau manifolds, about which I know little, and was wondering if these (or related complex manifolds, perhaps K3 surfaces) can be viewed as configuration spaces (or moduli ...
2
votes
0answers
139 views

When is the area of the convex hull of a tree-like linkage maximal?

This is inspired from this recent question. Given in the plane a tree-linkage (fixed length rigid edges, vertices are flexible joints, connected and no cycles) is there a simple description of when ...
9
votes
5answers
364 views

Is the area of a polygonal linkage maximized by having all vertices on a circle?

Consider a (non-stellated) polygon in the plane. Imagine that the edges are rigid, but that the vertices consist of flexible joints. That is, one is allowed to move the polygon around in such a way ...