Timeline for What are the $\inf$ and $\sup$ of the area of quadrilateral given its sides length?

11 events

when toggle format	what		by	license	comment
Jul 2 at 19:41	history	edited	pie	CC BY-SA 4.0	deleted 18 characters in body; edited title
Apr 16 at 14:49	history	edited	Martin Sleziak		edited tags
Apr 14 at 22:21	history	edited	pie	CC BY-SA 4.0	added 169 characters in body
Apr 13 at 12:56	answer	added	crow		timeline score: 2
Apr 13 at 1:21	answer	added	KhashF		timeline score: 5
Apr 12 at 23:53	answer	added	Corentin B		timeline score: 18
Apr 12 at 22:54	answer	added	Noam D. Elkies		timeline score: 19
Apr 12 at 22:30	comment	added	pie		@KhashF The quadrilateral need not to be convex at all and if $a+d<b+c$ I don't think you can make a quadrilateral like that notice that a,b,c,d are the side lengths in order around the quadrilateral.
Apr 12 at 22:23	history	edited	pie	CC BY-SA 4.0	added 60 characters in body
Apr 12 at 22:11	comment	added	KhashF		Further assumptions/clarifications are needed. For example, is the quadrilateral required to be convex? Another remark: the claim is that the infimum is given by the area of a triangle with sides $a,b,d-c$. The fact that such a triangle exists amounts to $a+d>b+c$. So I think there may be no nice answer in this very general way that you phrased your question.
Apr 12 at 20:36	history	asked	pie	CC BY-SA 4.0