Is a simple derivation for a formula publishable? I'm a high school student and recently discovered an interesting method of deriving the definition for $\arcsin z$ for the complex domain using integration. I typed it up for fun in LaTex and am wondering if this is worth trying to publish. It's nothing groundbreaking or complicated and certainly not a new result, but just interesting to note. It's about 4 pages long but could be condensed. Thoughts?
 A: By itself?  Probably not in a scholarly journal as an accepted article.
But, what you're doing shows a lot of initiative!  Kindly consider these suggestions:


*

*Start a mathematics blog and post your derivation to it.  Continue posting these novel derivations.  This shows you're serious because you're putting your work out there for anyone to see, and comment on.

*Participate here.  Try your ideas here, show where you're getting stuck, etc.  In general, this isn't so much the place to post things -- it's a place for questions and answers -- but you'll accelerate your learning with good questions here.

*Link to your blog in your profile.  Some people from here will visit, likely some who've dedicated several of your lifetimes to math and to teaching people math.  They're well-acquainted with how to nudge serious students of math in the right direction.

*Use your blog as a tool when talking to people about research opportunities.  Not many of your peers will be able to do this.  The research collaborations with professional mathematicians or with industry could lead to the publications you're looking for now.

A: First, if you rediscovered a method of proving something known, then I'd say that there's no hope in publishing it in a journal. You can share your thoughts with other students: make a presentation about it during the class. You can discuss it with your teachers.
Second, if discovered a new method of proving something known, and your proof is better (define better =) ) the the already known proof, then it might be worth publishing or presenting at a conference. Once again, discuss it with your teacher or share with us.
