Talk:Carpenter's rule problem

Name of article
The name of the article is wrong: it should be: carpenter's ruler problem

Could someone explain what this problem has to do with origami? —Keenan Pepper 23:25, 25 February 2006 (UTC)

Rule vs. Ruler
We (the authors Connelly, Robert; Demaine, Erik D.; Rote, Günter, cited in the references) believed it was "ruler" until Wlodek Kuperberk told us otherwise; he had asked a carpenter (or similar craftsman) and the correct term is carpenter's RULE. Google has about 2000 hits for "carpenters rule" but only about 900 for "carpenters ruler" (still a lot!). With apostrophe (') it is similar. See the Wikipedia article on "Ruler". Maybe someone can change the title back to rule as well.(G. Rote) --130.133.8.114 (talk) 14:25, 11 February 2009 (UTC)


 * Done. Igorpak (talk) 18:33, 11 February 2009 (UTC)

Polygon or open polygonal chain?
I read the article...

''Can a simple planar polygon be moved continuously to a position where all its vertices are in convex position, so that the edge lengths and simplicity are preserved along the way? A closely related problem is to show that any polygon can be convexified, that is, continuously transformed, preserving edge distances and avoiding crossings, into a convex polygon.'' Both problems were successfully solved by Connelly, Demaine & Rote (2003).

So, I understand, that in both cases we talk about poligons... What is difference?

I read mentioned paper

A planar polygonal arc or open polygonal chain is a sequence of finitely many line segments in  the  plane  connected  in  a  path  without  self-intersections. It has  been  an outstanding question as to whether it is possible to move a polygonal arc continuously in such a way that each edge remains a fixed length, there are no self-intersections during the motion, and at the end of the motion the arc lies on a straight line. ... A related question is whether it is possible to move a polygonal simple closed curve continuously in the plane, often called a closed polygonal chain or polygon, again without creating self-intersections or changing the lengths of the edges, so that it ends up a convex closed curve (see Fig. 1). We solve both problems here by showing that in both cases there is such a motion.

So here I see in first case NO POLYGONS, only in second case article refer to polygon. Jumpow (talk) 12:33, 4 November 2016 (UTC)


 * That's been corrected - but it now refers to the polygon version as the Carpenters rule problem - which seems unlikely. Surely thats the open chain problem ? - Rod57 (talk) 13:13, 8 November 2017 (UTC)

When first defined ?
When was this first described as a problem ? - Rod57 (talk) 12:54, 8 November 2017 (UTC)


 * Folding and Unfolding Linkages, Paper, and Polyhedra Demaine (2001?) says "The questions of whether every polygonal arc can be straightened in the

plane and whether every polygon can be convexified in the plane have arisen in many contexts over the last quarter-century. In particular, they were posed independently by Stephen Schanuel and George Bergman in the early 1970’s, Ulf Grenander in 1987, William Lenhart and Sue Whitesides in 1991, and Joseph Mitchell in 1992. In the discrete and computational geometry community, the arc-straightening problem has become known as the carpenter’s rule problem because a carpenter’s rule folds like a polygonal arc". - Rod57 (talk) 14:00, 8 November 2017 (UTC)

A different Carpenters rule problem
and describe it as the decision problem of folding a chain of specified line segments into a specified max length. (an NP problem.) - Rod57 (talk) 13:46, 8 November 2017 (UTC)

Example
Can we have a diagram showing why its called a problem ? or explain that it's just a rigorous mathematical proof that's a problem ? - Rod57 (talk) 12:54, 8 November 2017 (UTC)