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Ok, I read through the proof, and I think I understood it. Thanks for posting this! Until the authors' work is submitted to a journal and reviewed, it's hard t

Ok, I read through the proof, and I think I understood it. Thanks for posting this! Until the authors' work is submitted to a journal and reviewed, it's hard to say everything claimed here is definitely correct & new. Update: Nice video on the proof: https://www.youtube.com/watch?v=nQD6lDwFmCc https://www.youtube.com/watch?v=nQD6lDwFmCc I like what they did :) Seems legit to me. Btw, law of sines can be proven independently of pythagoras. So using that as a step is ok. https://en.wikipedia.org/wiki/Law_of_sines https://en.wikipedia.org/wiki/Law_of_sines

hgsgm 3y ago
It's obviously correct (it's basic high school math; as with most proofs, the cleverness is in the construction, not the computation) and nearly obviously new or at least newly published. (There are many easily searchable collections of proof, but not everyone published their proof of a theorem already proved and published over 400 different ways)
ummonk 3y ago
It's definitely correct, and quite trivial to verify. It's possible it has been discovered before, but none of the proof compilations I've seen (e.g. cut-the-knot) has it, and the trigonometric proofs I can find involve using angle-sums (https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf). This is definitely a much more elegant proof than the angle-sum proofs.
- starchild_3001 3y ago
  Correctness might be there. But there are also some grandiose claims in the abstract ("“There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.”) and the argument being novel. I don't have a way to verify these two. That's what the peer review is for. ------------ update: This video refers to another trigonometric proof that doesn't rely on sin^2 + cos^1 = 1. https://www.youtube.com/watch?v=p6j2nZKwf20 https://www.youtube.com/watch?v=p6j2nZKwf20 I would write a more modest abstract for this work. Just my $0.02.

hgsgm 3y ago

It's obviously correct (it's basic high school math; as with most proofs, the cleverness is in the construction, not the computation) and nearly obviously new or at least newly published. (There are many easily searchable collections of proof, but not everyone published their proof of a theorem already proved and published over 400 different ways)

ummonk 3y ago

It's definitely correct, and quite trivial to verify. It's possible it has been discovered before, but none of the proof compilations I've seen (e.g. cut-the-knot) has it, and the trigonometric proofs I can find involve using angle-sums (https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf). This is definitely a much more elegant proof than the angle-sum proofs.

starchild_3001 3y ago
Correctness might be there. But there are also some grandiose claims in the abstract ("“There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.”) and the argument being novel. I don't have a way to verify these two. That's what the peer review is for. ------------ update: This video refers to another trigonometric proof that doesn't rely on sin^2 + cos^1 = 1. https://www.youtube.com/watch?v=p6j2nZKwf20 https://www.youtube.com/watch?v=p6j2nZKwf20 I would write a more modest abstract for this work. Just my $0.02.