# Planar geometry on MO

"Planar geometry" here is 2-dimensional Euclidean geometry, usually used as Olympiad geometry problem, its objects just be a bunch of lines and circles, it has no Combinatoric aspect and not used to solve another research problem like convex geometry.

Is planar geometry question suitable for MO? This type of question usually can be solved just by a computer and almost have no relation to other field of Mathematics.

Sometimes I see planar geometry on MO and it annoys me a lot because I can't understand what its research value is. Moreover, it even has some upvote! Example.

• "its objects just be a bunch of lines and circles". Well, the same can be said for Pascal Exagram Theorem, that is by no means a trivial result (even if not "research-level, nowadays). Ï guess the answer depends on the specific question, as usual. And what do you mean by "This type of question usually can be solved just by a computer and almost have no relation to other field of Mathematics"? Jul 27, 2022 at 9:30
• @FrancescoPolizzi Not even the problem is just a bunch of lines and circles, its "standard" solution is too. The proof is just you proof some point colinear or concylic, some angle or some ratio of line segments length are equal,... "Solve by a computer" mean math.stackexchange.com/questions/31192/…. And if you say the problem is too complicative to solve by algorithm, how do you feel if someone put some random Diophantine equation on MO? Jul 27, 2022 at 10:13
• Polynomial identities may be checked on a computer but finding polynomial identities which are interesting can be a research mathematical problem, and sometimes the right polynomial identity is the key to solving a deep research problem. I think the situation with plane geometry is the same. In any case MO should err on the side of inclusion. Jul 27, 2022 at 21:20
• @WillSawin So you mean putting (spamming) Olympiad, exercise, logic puzzle, random conjecture,... on MO is ok because who know, some identity, trick or theory magically come out and that the key to solve deep research problem?! Jul 28, 2022 at 0:03
• There are several conditions that determine whether a question is OK on MO. Saying "all questions in X field are OK" and "all questions in X field are not OK" are both wrong. In this case the question was not asking to prove the statement (which would be dubious when there is a well-known algorithm to solve all such problems) but for historical context (which the answer has now provided). Jul 28, 2022 at 0:11
• For each finite group $G$, the claim that $G$ is a finite simple group can be checked by computer. If MO existed during the era before classification of finite simple groups and someone posted a question "I found this finite simple group, is it already known?" that would be a very good question. But that doesn't mean that undergraduate exercises in group theory are acceptable. Of course this question doesn't have as much relevance to broader mathematical research as the finite simple group one. But it has enough to be over the line. Jul 28, 2022 at 0:13
• @WillSawin it seem means that we can put anything related to math if we question the right way?! with a good "question skill", i guess anyone can put their answer enough to be over your line. Question skill is important but the core is far more important. May I misread you but your answer be like "that question is ok just because it not seeking for solution". Jul 28, 2022 at 1:06
• Surely there are some questions no formulation of which would be acceptable on MO. And if someone were to ask a lot of similar questions, I think the threshold could get higher. But I don't see what the benefit would be to pushing the well-written plane geometry questions, which don't come in enormous numbers, off the site, compared to the cost of making the site less welcoming for newcomers. Jul 28, 2022 at 1:20
• One way to think of this is that the primary goal of getting rid of bad questions is to make the site pleasant for question-answerers, to keep as many experts around answering questions as possible for the questions that are important in someone's research. Thus questions that are fun, or, more precisely, likely to be considered fun by someone who also enjoys answering questions relevant to active research, will generally not be deleted. They don't cause the same problems that dull questions do! The skill of making your question fun will protect it, but this is a feature, not a bug. Jul 28, 2022 at 1:23
• I really don't think pushing planar geometry question have any significant cost. But yeah, keeping those question don't have any significant harmful too. Keep MO being fun and beauty may be good as you say. Jul 28, 2022 at 1:31
• Possibly the simplest answer to what is appropriate on MO is "what the community welcomes." This can change over time, is never universal (in the sense that some users, again changing over time, will always disagree with the community), and, as @WillSawin points out, it can rarely be boiled down to axioms about what broad types of questions are or are not acceptable. But, in the end, if a question has more upvotes than downvotes, then that means that the community has received it overall positively, and that is probably the only real way to judge its appropriateness. Jul 30, 2022 at 21:03
• It may be more helpful to break this down by user than by tag -- and when a user's ratio of questions to answers is this high (85 to 7), I'd like to see them apply more quality control to their questions. Sep 1, 2022 at 1:38