Paper by Martin L. Demaine

Therese Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, and Sue Whitesides, “A Note on Reconfiguring Tree Linkages: Trees can Lock”, Discrete Applied Mathematics, volume 117, number 1–3, 2002, pages 293–297.

It has recently been shown that any polygonal chain in the plane can be reconfigured to lie on a straight line, and any polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two configurations that are not connected by a motion. Indeed, we prove that an N-link tree can have 2Ω(N) equivalence classes of configurations.

The paper is 5 pages.

The paper is available in PostScript (360k) and gzipped PostScript (68k).
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Related papers:
LockedTreeTR (On Reconfiguring Tree Linkages: Trees can Lock)
CCCG98c (On Reconfiguring Tree Linkages: Trees can Lock)

Related webpages:
Erik Demaine's Carpenter's Rule Theorem

See also other papers by Martin Demaine.
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Last updated November 17, 2022 by Martin Demaine.