Timeline for Constructing a polygon of $n$ facets from a set of positive values representing the length of the facets [closed]

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Mar 20, 2016 at 5:49	history	closed	Ilya Bogdanov Wolfgang Alex Degtyarev Alexey Ustinov Ryan Budney		Not suitable for this site
Mar 17, 2016 at 18:58	review	Close votes
Mar 20, 2016 at 5:49
Mar 17, 2016 at 9:12	vote	accept	P. Bu.
Mar 17, 2016 at 6:59	answer	added	Manfred Weis		timeline score: 1
Mar 17, 2016 at 6:41	comment	added	Fedor Petrov		Another result in this direction is that under above necessary condition there exists unique cyclic polygon with given sides (in given order).
Mar 17, 2016 at 0:30	comment	added	Joseph O'Rourke		See the earlier related MO question and answer here, which cites references. The condition you mention allows not only construction of a polygon, but of a convex polygon, and in fact, a triangle.
Mar 17, 2016 at 0:03	comment	added	Fedor Petrov		Of course it is enough. You may do it by induction: having (convex) $(n-1)$-gon with sides $a_1, a_2,\dots,a_{n-2},a_{n-1}+a_n$ we may replace triangle with sides $a_{n-1}+a_n,a_{n-2}$ and some third size $x$ to a quadrilateral with sides $x,a_{n-2},a_{n-1},a_n$, which is a union of two triangles with sides $a_{n-1}+a_n-\varepsilon,a_{n-2},x$ and $a_{n-1}+a_n-\varepsilon$, $a_{n-1},a_n$.
Mar 16, 2016 at 23:55	comment	added	Steve Huntsman		As an aside, projecteuclid.org/euclid.jdg/1214457034 discusses the relevant moduli space
Mar 16, 2016 at 23:42	history	asked	P. Bu.	CC BY-SA 3.0