Talk:Hinged dissection
Add topic | A fact from Hinged dissection appeared on Wikipedia's Main Page in the Did you know column on 29 December 2013. The text of the entry was as follows:
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To-do
[edit]There should be some mention of piano-hinged dissections, which Frederickson has also written a whole book (and this nice paper) about. I may get around to this eventually but I don't think I understand them well enough right now. Might such dissections be properly considered more an issue of mathematical origami? Anyone who wants to tackle this can feel free. ∴ ZX95 [discuss] 16:29, 22 December 2013 (UTC)
Hinged dissections result generalized
[edit]I just found this post on Math Overflow [] that reports a paper that generalizes the hinged dissection result: [1]
"Abstract. We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years."
I'm not familiar enough with the math to add a citation (or does it fall under no original research?) Sesquiannual (talk) 03:32, 10 February 2019 (UTC)
- The book containing this paper is already been cited in the article, but was missing the chapter title. — Saung Tadashi (talk) 01:46, 11 February 2019 (UTC)
References
- ↑ Abbott, Timothy G.; Abel, Zachary; Charlton, David; Demaine, Erik D.; DeMaine, Martin L.; Kominers, Scott Duke (2012). "Hinged Dissections Exist". Discrete & Computational Geometry. 47 (1): 150-186. doi:10.1007/s00454-010-9305-9. Retrieved 10 February 2019.