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I am a university AP and I like composing problems (not for kids, not for practice). Oftentimes I don't know whether or not the problem has been considered or solved by other mathematicians. Is mathoverflow the best place to explore that?

For example, a geometry problem. There are finitely many lines on the plane, none parallel. Each line is divided into 2 infinite rays and several segments by the intersections with other lines. It is called a monotone line if the lengths of these segments are increasing or decreasing along the line. If there are only 1 or 2 segments it is automatically monotone.

The question is to give a classification if all lines are monotone.

It seems not complicated, but anyone has thought about it or similar problems?

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    $\begingroup$ As the proposed questions do not concern math research, they would probably fit better on math.stackexchange.com than on MO. $\endgroup$ – Gerry Myerson Oct 8 '17 at 11:39
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    $\begingroup$ The term in the literature for your collection of lines is an arrangement of lines. I do not recall your particular question being addressed. $\endgroup$ – Joseph O'Rourke Oct 8 '17 at 13:32
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    $\begingroup$ What kind of problems are considered as research problems? Problems that are interesting and hard? $\endgroup$ – Haoran Chen Oct 9 '17 at 3:23
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    $\begingroup$ Roughly, problems which are interesting for mathematicians. That the problems are hard is neither necessary nor sufficient. In case of doubt, just post your question. And bear in mind that how people interact with you may also depend e.g. on whether you ask your question as user143870 or under your name. $\endgroup$ – Stefan Kohl Oct 9 '17 at 9:15
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    $\begingroup$ As @StefanKohl says, it is definitely a "show of good faith" to ask questions under one's own name, and maintain a registered user status, rather than flitting-in under a different unregistered user name various days. Having an established user-name, and a history of seriousness, greatly helps one's credibility, and, thus, the seriousness of responses you'll get. $\endgroup$ – paul garrett Oct 14 '17 at 0:23
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    $\begingroup$ @HaoranChen, my experience from being on this forum as not mathematicion is that "research problems" are neither interesting nor hard. The "research problems" are such problems which are currently hot topics on agenda of working mathematicians. You do not guess it by your own. Be prepared that when you ask the question which just come to your mind by curiosity, they will be closed here. They might be hard and interesting :) $\endgroup$ – Marek Mitros Oct 17 '17 at 12:09
  • $\begingroup$ @MarekMitros, you are right, and they will be closed here :) unless someone, yes, someone finds them useful and he has the power to make them hot... $\endgroup$ – Haoran Chen Nov 4 '17 at 14:20
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    $\begingroup$ @MarekMitros We make of MO just what we make of it. What you describe is an observable phenomenon, but the opposite tendency is also clearly present. So, all I can say to the OP is "use common sense when asking, you are judged by your common sense and taste in your questions more than by anything else." $\endgroup$ – fedja Nov 15 '17 at 14:58
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I think part of the expectation is that you should have done some "research" into the question yourself before posting, but it doesn't have to be a serious amount of research, or about an area in which you are an expert. For instance, my most recent question Integrality of iterates of rational functions was something I just wondered about randomly, not related to my own research. So thought about a little myself and tried googling first, and didn't see a clear answer and tried asking here (with the knowledge that I was asking from a very naive perspective, but I had some idea the question that other mathematicians think it an interesting question). It turned out the problem was solved over 20 years ago, and was easy to answer for someone who knew about arithmetic dynamics, but not for me.

The point is we don't want the site watered down with poor questions, and if you have looked into the question for yourself first, and still can't answer it, probably you can at least ask a better question (and, as mentioned in the comments, using your real name and establishing a track record can help get your questions taken more seriously).

Of course, the question should not just show that you've put some effort into it, but for this site it should be of interest to research mathematicians. It's hard to know in advance, if you're not a mathematician or not very familiar with MO, what will be of interest. (In fact, often when we write papers, we don't know whether they'll be of interest or not!) But a decent rule of thumb is that if the question seems to be in the realm of college-level math or lower, then try asking on Mathematics.SE, but if you have no luck there or it seems to require more advanced math, try asking here.

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