Close. I sent it to rrusczyk around the time it got accepted by the Monthly. I wanted him to see it because AoPS was playing a huge role in my mathematical education at the time, and was happy when he wanted to post it on the website.
I did a lot of Googling to see if it turned up, showed it to my math teachers and my mathematician parents, sent it off to the editors, and hoped for the best. 17 years have gone by without anybody pointing out an earlier instance of the proof to me, so it seems pretty safe at this point.
I appreciate that, but it requires creating an account, and for people who have a gazillion other things to be doing, taking the time to create Yet Another Account on Yet Another System just for the one article is something most people will pass on.
It may not have a financial cost, but it certainly has an opportunity cost, and contributes to "Account Fatigue".
But loved the proof of Heron's formula, and I'm pleased to be able to say thank you in person, and make sure I give credit when I use it for the Math Club talks I do.
Great work ... feel free to contact me if you are so inclined, or put an email address in your profile.
Hi! I wrote that proof back in 2007, half of my lifetime ago. It's neat to see it discussed again.
My original writeup was longer and included several of the details that you mentioned. However, the editors of the American Mathematical Monthly condensed it, presumably so that it could be published as a "filler" that would take up less than a page. What you see is their rewrite of my work.
In fairness to them, the stuff that's left out is well known to people who think about incircles and excircles and thus not really new. For instance, it's used in the proof of Heron's formula by similar triangles.
There were some things that I would not have put that way on my own. For instance, at that point in my life, I had actually been trained not to use the word "clearly" like it's used here.
But who was I, a high school student, to quibble with the editors of the American Mathematical Monthly? I was thrilled that they wanted to publish my work. No regrets.
Hey it's nice that you found this post and replied! You shouldn't have any regrets indeed, and I guess that style has its place for a "filler" article, even though calling it a filler is not so nice...
Make it a rant about the editors—if they had been your "mistakes" they should have corrected you, and I am happy to learn that they weren't yours in the first place.
