Paper by Martin L. Demaine

Reference:

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.

Abstract:

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 2^Ω(N) equivalence classes of configurations.

Length:

The paper is 5 pages.

Availability:

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