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I'm a 10th grader who is extremely interested in Mathematics and I frequently come across some interesting (at least, to me) results while doing some Math problem and sometimes I want to get an expert-level opinion on that result.
For example, I was recently thinking about how one would go on about defining a function that gives a graph like the one given below :

enter image description here

I successfully defined such a function using a combination of the floor function, ceiling function, fractional part function and the signum function. It was pretty interesting for me.
Another time, I discovered a simple derivation for the quadratic formula and once, a derivation for the compound angle identities in Trigonometry

These are some examples of when I wanted to share these and get some reviews/opinions about the results that I had obtained.

So, basically, is there a website for Mathematics like Code Review for Coding in the Stack Exchange Community?

Thanks!

PS : If you're wondering what the functions is, it's given below : $$f(x) = \text{Sign}\Bigg(\Bigg\{\dfrac{\lceil x \rceil}{2} \Bigg \} - a \Bigg) \text{, where } 0 < a < 0.5$$ $$\text{Here, }\{ x \} \text { is the fractional part function which is defined as } \{ x \} = x - \lfloor x \rfloor$$ $$\text{And Sign}(x) \text{ is the signum function, which gives the sign of the input, and } 0 \text{ in case the input is }0$$

Edit : I recently thought of a much simpler version of the function that I talk about above. It is : $$f(x) = \cos(\lfloor x \rfloor \cdot \pi)$$

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    $\begingroup$ A better and clearer definition would be to not insist that it be given by a single formula and to say that $$f(x)=\begin{cases}1&\mbox{ if }2n<x\leq 2n+1\\-1&\mbox{ otherwise}.\end{cases}$$ $\endgroup$ – Matt Samuel Jun 16 '20 at 20:47
  • $\begingroup$ An addition though : "Where $n \in \Bbb Z$". Actually, the reason that I insisted on a Mathematical definition of the function was so that it can be graphed using a graphing calculator and embedded in a computer program with a mathematical approach. Thanks for the suggestion! $\endgroup$ – Rajdeep Sindhu Jun 16 '20 at 20:52
  • $\begingroup$ Is "check my work" question not allowed? We have a tag specified for that. $\endgroup$ – Arctic Char Jun 16 '20 at 20:55
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    $\begingroup$ I am familiar with the solution-verification tag and in fact, have used it a few times too. As far as I know, this question : math.stackexchange.com/questions/3704308/… was closed till some time ago for the reason : Homework and check my work type questions not allowed. It's re-opened now though. Also, wouldn't a separate site (like Code Review for reviewing programs) be nice? $\endgroup$ – Rajdeep Sindhu Jun 16 '20 at 21:03
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    $\begingroup$ I looked at the timeline and it doesn't appear that the question was ever closed. The reason is invalid in any case, because both homework and check-my-work questions are allowed. $\endgroup$ – Matt Samuel Jun 16 '20 at 21:34
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    $\begingroup$ @MattSamuel I'm sorry for the misleading info. Looks like I can't recall the question which was closed for being a 'check my work' type question. Maybe (and most probably), it wasn't even on Mathematics SE. $\endgroup$ – Rajdeep Sindhu Jun 16 '20 at 21:43
  • $\begingroup$ Then get rid of the first sentence of your post, @RajdeepSindhu ! $\endgroup$ – amWhy Jun 16 '20 at 23:30
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From the Help Center article Can I answer my own question?:

Yes! Stack Exchange has always explicitly encouraged users to answer their own questions. If you have a question that you already know the answer to, and you would like to document that knowledge in public so that others (including yourself) can find it later, it's perfectly okay to ask and answer your own question on a Stack Exchange site.

It looks like you have a question ("How can I define a formula for a function with this graph, without resorting to piecewise definitions?") and an answer, so by Stack Exchange rules you're allowed to post it as a question. It might even be that another users comes up with a better/more clever answer than you.

One caveat: there might be other users which don't think it's a useful Q&A pair, and they might downvote it for that reason; my experience across the network is that self-answered questions are held to a higher standard than regular ones.

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  • $\begingroup$ Thanks! Answering the question yourself sounds like a good idea. $\endgroup$ – Rajdeep Sindhu Jun 16 '20 at 21:41
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    $\begingroup$ Rajdeep, please pay close attention to this answer's last paragraph: "One caveat: there might be other users which don't think it's a useful Q&A pair, and they might downvote it for that reason; my experience across the network is that self-answered questions are held to a higher standard than regular ones." $\endgroup$ – amWhy Jun 16 '20 at 23:28
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    $\begingroup$ The meta question says "sometimes I want to get an expert-level opinion on that result" or to ask for something like the code review SE - I think that posting a Q&A pair is not a good solution for these goals, because answers can only receive comments and votes as feedback - which is rarely enough to contain a substantive review and where there's not a particularly strong expectation that the feedback will be constructive or geared towards improving the poster's understanding of mathematics. $\endgroup$ – Milo Brandt Jun 17 '20 at 0:01
  • $\begingroup$ @MiloBrandt Till now, Q&A seems to be the best option I have and something focused on reviews as much as Code Review SE would be more than sufficient. Please let me know if you have any other suggestions. $\endgroup$ – Rajdeep Sindhu Jun 19 '20 at 19:01

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