(I wrote this post a while back so its no longer NEW. More important--- if there has been a follow-up to the story that is not in my post, let me know.)
We have something NEW and something OLD about the Pythagorean Theorem. Now all we need is something BORROWED and something BLUE.
NEW
Two high school students have a new proof of the Pythagorean Theorem, see here. (An anonymous commenter provides a pointer to their published article in the American Math Monthly.)
They used trigonometry. Oh wait, that sounds circular since Trig is based on the Pythagorean Theorem. While this is a fair question to ask about the theorem, it has recently been accepted for publication and looked at carefully (those two are not equivalent) so it seems to be correct.
The Pythagorean Theorem is an often-proved-theorem. Often an often-proved-theorem has proofs that use hard math (e.g., proofs that primes are infinite using Ramsey Theory, see my post on that here). However, the new proof of PT seems to be elementary.
Kudos to them!
OLD:
Pythagorean theorem found on clay tablets 1000 years earlier than Pythagoras: see here.
My students would ask me
How come Pythagoras didn't go to arXiv to see if someone already had the theorem?
Published in American Math Monthly in 2024. Seems to be genuinely new proofs (but the hype about it being the first published "trig" proof was incorrect). https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2370240
ReplyDeleteWhy is the hype incorrect?
ReplyDeleteIn the American Math Monthly article, the authors acknowledge "we have no idea how to draw a clear line between “trigonometric” proofs of Pythagoras’s theorem and non-trigonometric proofs." They also cite two previously published proofs that fit their proposed criteria for "trig" proofs.
ReplyDeletethanks for clarifying!
Deletethe more interesting part. none of them ended up going into mathematics or engineering. thanks for sharing. Sorry I did not have the time to look at the proof yet.
ReplyDeleteI will expand on that: Ne'Kiya Jackson is getting a doctoral degree in pharmacy. Calcea Johnson is studying environmental engineering.
DeleteIf people who are great at math end up doing something else, is that good or bad? Of course its their choice. What is good for society? I leave that as an open question and a possible later blog post.