I'm an undergraduate student and I believe I found another proof of Heron's formula. I have a bunch of questions:
I would like to publish this "proof" (I haven't found mistakes yet) in some magazine. But as you would expect I don't want to discuss the proof with someone else from my university (perhaps they can steal it?) or who knows. Anyway I'm confused what to do, would it be wrong if I write the paper in .tex and submit it to some magazine? what is the typical procedure in this case? with whom shall you discuss your "proof" ? is it common to submit "proofs" of theorems and then be noticed by the editor that your proof is actually wrong?
Can you please give some advice?