Two students who discovered a seemingly impossible proof to the Pythagorean theorem in 2022 have wowed the math community again with nine completely new solutions to the problem.
While still in high school, Ne'Kiya Jackson and Calcea Johnson from Louisiana used trigonometry to prove the 2,000-year-old Pythagorean theorem, which states that the sum of the squares of a right triangle's two shorter sides are equal to the square of the triangle's longest side (the hypotenuse). Mathematicians had long thought that using trigonometry to prove the theorem was unworkable, given that the fundamental formulas for trigonometry are based on the assumption that the theorem is true.
Jackson and Johnson came up with their "impossible" proof in answer to a bonus question in a school math contest. They presented their work at an American Mathematical Society meeting in 2023, but the proof hadn't been thoroughly scrutinized at that point. Now, a new paper published Monday (Oct. 28) in the journal American Mathematical Monthlyshows their solution held up to peer review. Not only that, but the two students also outlined nine more proofs to the Pythagorean theorem using trigonometry.
I'm constantly amazed by the number of things that we have assumed was true simply because we were taught that in school and never questioned it.
Pythagorean theorem has over 100 proofs, they are just geometric one, this is the first trigonometric one. The reason it is impressive is that the pythagorean theorem is foundational to trigonometry, so any attempt at a trigonometric often calls on the pythagorean theorem implicitly.
One might need to prove that a trigonometric proof isn't equivalent to any geometric proof. Somehow the premise here "a proof based on the sine law" doesn't inspire that confidence for me as sine law has equivalent formulations in geometry.
That said, I'd also say that the boundary between geometry and trigonometry isn't a particularly necessary one, and the work of these young girls exposes this.
Do check out the quote from the girls' research paper I put in the other reply thread. Even they couldn't believe they actually did it. From my very basic understanding of what they achieved, it is something pretty monumental.
Yo, me too!
I like to tell people about how everything they think they know is actually stuff someone told them and they believed based on the presentation. School is certainly a good look right after you leave church, yeah? Seems very sane and rational. Tons of the stuff you "learn" is self evidently correct which helps you believe all the rhetoric that props up nationalism and whatnot.
There's no telling what's real or made up to keep us in line as individuals, and good luck gathering free thinkers and maintaining information integrity with a group.
Oh for god sakes. The vast majority of things you learn in school, that aren’t basic things like language and physical education anyway, actively have you participate in the process of working through to the correct answer.
I’m not going to say that you remember the process. But you didn’t spend weeks in class learning how to punch numbers into a calculator, you were taught about the process, why that process works, and literally hand held through the process of you being the one to come to the eventual answer.
This applies to many subjects, like science and math.
I will admit, this may not be the case for all classrooms. But I can say with certainty that this is the case for North America, and most if not all western nations.
If you truly think you’re simply told what to think and turned out to the world… you likely didn't actually pay attention.
They're brainwashing everyone in history class, but it's okay because they're also teaching us the little bit of math we need to operate an industrial saw as a dead end job?
I think we didn't go to the same schools.
We didn't get enough education for operating a saw.
You didn't learn to convert fractions and decimals? Damn, your school sucks.
You tell me.
At least I missed the wave of paedophilia that's apparently getting uncovered in that country's school system nowadays.