Talk:Triangle is Convex Set

I don't know the formalisms involved here. But that normally means they should be linked. There are betweens all over. I understand what they mean intuitively, but I don't know a formal definition. I don't know what it means for a side to "become" a line segment. Then there's the matter of the interior of a triangle. That's obviously based on a geometric, rather than topological, definition of interior (as the topological interior of a triangle is empty), but there's no link to that either. Now, I haven't taken a serious geometry class since seventh grade (the one I took last year was mostly fluff) so maybe that's the problem. --Dfeuer (talk) 12:10, 4 February 2013 (UTC)

Realizing you don't know anything is usually a path to greater understanding. :)

More seriously, the formalities of geometry is not my forte either. I'm merely putting up these theorems so I can use them for my complex analysis section. I've tried to adress the problems of "between" and "become". As for the definition of "interior", it's the definition from the Jordan Curve Theorem, where the boundary of the triangle is considered as a Jordan Curve. Since User:Jshflynn also has uploaded pages about Jordan Curves, I've contacted him to ask whether we should collaborate on the subject. Once we have some definitions and theorems about interiors of Jordan Curves, I intend to go back and revise this theorem once again. --Anghel (talk) 16:01, 4 February 2013 (UTC)

A better approach, rather than try to replace technical terms like "between" with a set of even more intuitive explanations, would be to add "between" as a link to a definition. It will appear redlinked, but the job will be done and it will then be up to the experts in geometrical axiomatics to finish off this tricky stuff.

I suggest that the version of this page be reverted to what it was before the question about what "between" means, thereby improving the clarity of the page.

Also, for future reference: if an undefined term is used on a page, it might be worth adding those links directly, rather than adding an "explain" template - it saves misunderstanding and cuts down on work to be done. --prime mover (talk) 16:38, 4 February 2013 (UTC)

You are right (second point). Will adhere. --Lord_Farin (talk) 16:49, 4 February 2013 (UTC)

The JCT isn't really necessary to explain the notion of "interior" for polygons, is it? --Dfeuer (talk) 16:51, 4 February 2013 (UTC)

There's little to explain, or so I hope. But to make it rigorous there's (IIRC) quite a bit of work involved - not to mention the complications of passing to higher dimensional constructs. --Lord_Farin (talk) 16:56, 4 February 2013 (UTC)