Talk:Polygonalization

{{GA|20:13, 19 February 2023 (UTC)|topic=Mathematics|page=1|oldid=1140227520}}

{{DYK talk|17 March|2023|entry=... that a simple polygon through all the points of a three-by-three grid must pass straight through some of the points, rather than turning at each of them?|nompage=Template:Did you know nominations/Polygonalization}}

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Generation: I thought this was solved?

I read the paper "Connecting Polygonizations via Stretches and Twangs" [https://arxiv.org/abs/0709.1942] at least ten years ago. I thought that this set of moves sufficed to connect the space of polygons for a fixed set of points in the plane? 73.5.136.47 (talk) 18:24, 22 November 2022 (UTC)

:They connect a larger space, the "polygonal wraps". The intermediate steps of the connection paths are not polygonalizations. If all you want to do is connect a larger space, the problem is much easier. For instance, the polygonalizations are contained in the space of planar straight line graphs, which are trivially connected by edge insertions and deletions. —David Eppstein (talk) 18:41, 22 November 2022 (UTC)