New Orleans teens make mathematical discovery unproven for 2,000 years
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- Опубликовано: 11 окт 2024
- It takes a special kind of student to outsmart 2,000 years of mathematicians -- at St. Mary's Academy, they have two.
Calcea Johnson and Ne'Kiya Jackson just gave a presentation to the American Mathematical Society's Annual Southeastern Conference. They say they've proved Pythagoras' Theorem can be proven with trigonometry -- something that many thought was impossible.
It might not surprise you to hear they were the only high school students in the room.
"It's really an unparalleled feeling, honestly, because there's just nothing like being able to do something that people don't think young people can do," Calcea said. "A lot of times you see this stuff, you don't see kids like us doing it.
If you need a refresher on Pythagorean Theory, you're not alone.
Calcea and Ne'Kiya explained it to me like this: Basically, trigonometry is based on Pythagoras' Theorem (A^2 + B^2 = C^2, sound familiar?), so using trigonometry to prove Pythagoras's Theorem is what's known as circular logic.
An idea can't prove itself.
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I would have loved to hear the girls, instead of the news anchor, explain their story and the theorem. They deserve the screen time for their hard work! Stay focused on your pursuit of knowledge and goals girlies!
Incredible story. Not everything your math textbook tells you is correct, particularly about the history of mathematics. I'd love to see this proof in detail.
Hey Presh! Saw this video in your community post
Hey Presh, would love to see a follow up video about this on your channel (walkthrough of the proof!)
Hey, it you!
Yes. Make follow-up video, Presh
Where can I find their proof?
I hope college recruiters are watching these two prizewinner teens. Go, kids!!
They probably on they way to win a noble prize.
I hope you guys are being sarcastic. This story is pure 💩
@leslie landberg why..lol😂😂😂
@@leslielandberg5620 you are right - even the reporter erroneously shows a right triangle and calls it trigonometry ( the right triangle is geometry )
furthermore, I was able to use trigonometry to proof pythagorean theorem years ago - there is nothing new here - just propaganda
@@leslielandberg5620 Lol angry racist Karen.
My favorite part was when they described how they found it
Mine was them showing their work and the formula they developed. 🤦♂️
@@weldermandanthe publish their findings bud
As someone currently in College Calculus 2 and might be minoring in math for engineering, I really want to see more of how they proved it.
Pause the last few seconds of the whiteboard in the video before the closing comments begin to see some details
You should know better. JFC
I've been looking for the past hour trying to find their work somewhere online
Just more BS, inclusive horse crap
@Redrum Susan after they’ve been through- systemic racism, oppression etc. you continue to demand ‘proof’? We all need to be more sensitive to their feelings
Congratulations to Calcea, Ne'Kiya, and their parents and teachers!
So why did you guys keep their discovery a secret? I wanted to know HOW they did it what’s the math behind it let’s see
It needs to be verified by the proper wizards.
I bet they got it right.
There's nothing to see.
THERE IS NO DOUBT WITH RESPECT THE VERACITY OF THESE BRILLIANT STUDENTS' ACCOMPLISHMENT! IT IS REAL! IT IS CORRECT! AND IT WAS THOUSANDS OF YEARS IN THE MAKING BY TWO YOUNG BLACK FEMALES! Words cannot express the powerful things I am feeling now.
When you look at the segment beginning @1:30 in the video, You can see the model that was solved by a convergence function. The figure you see projected is the essence of the solution. BRILLIANT! BRILLIANT! The Black Females never to be surpassed! Everything is verified and codified!! !!
@@GottaWannaDance Words cannot express the powerful things I am feeling now. When you look at the video, spot near the beginning so you can see the model that was solved by a convergence function @1:30 in the video! BRILLIANT! BRILLIANT! The Black Females never to be surpassed! Everything is verified and codified!!
THERE IS NO DOUBT WITH RESPECT THE VERACITY OF THESE BRILLIANT STUDENTS' ACCOMPLISHMENT! IT IS REAL! IT IS CORRECT! AND IT WAS THOUSANDS OF YEARS IN THE MAKING BY TWO YOUNG BLACK FEMALES! Words cannot express the powerful things I am feeling now.
Super disappointed this story isn't being covered by any other new sources. Thank you guys so much for shedding light on it!
@@Nozomi621 You sound silly. It has only ever been proven using it's own equation; while doubling as it's own definition. Which is circular reasoning if you were paying attention. Most other theorems can be proven more than one way. The pythagorean theorem proves itself. No one said they solved it. They simply found another way to prove it. Which had never been done before. If you don't know what you're talking about just say that next time smh.
@@Nozomi621 "The worst journalism you've ever seen" 😂😂😂😂... What a drama queen you are lmaoo.... Try watching TYT during Trump's election. Now THAT'S bad journalism. This was a fun, light hearted story about two young, determined, incredibly smart and capable children who did something pretty cool. No way on earth this was "the worst journalism you've ever seen". There was nothing "woke" or controversial about it. Take a chill pill dude. Maybe find a girlfriend or something lol.
@@GodOfDestructionVegeta27 💯😉
It’s not a news source per se but it’s being shared on IG
@@she_sings_delightful_things He deleted his idiotic comment lol.
This is wonderful. Mathematics is a door for infinite opportunity. Good job girls.
i'm as impatient as everyone to see the full thing but this is academia gang. many of those present were impressed and taking notes. the girls' work is likely being studied in more detail and run through a bunch of computations to confirm that it works. it's like saying "i'm doing a study on x and y and z" and then being expected to hand out the data before it's been peer reviewed. (that has happened before and it's never ended well). the girls' work has made it this far and has been shown to be worth the time of experts in the subject which should be enough for now. i'm excited for the results!
That's what I was thinking every time I saw a comment asking 'where's the math?'
That’s a good explanation. I really would like to see it though so I could tinker around with it myself. I don’t expect it to be published as fact yet.
I mean work can be published before it's been peer reviewed. It just comes with the warning that it hasn't been peer reviewed. The most likely thing is that there is a flaw and no one will hear anything about this again. It's great to encourage young minds and I'm glad people are. However, I don't really understand why they are being placed upon a pedestal before they've actually published the proof. Already there are numerous stories claiming they've shaken math to its core but it's just sensational journalism to get clicks. Nothing more
you can find a video on youtube where a guy reconstructed this proof from some of their presentation slides. it's also worth looking at the comments under the pinned one.
@@fumbducks (like when a random dude said he had proven the collatz conjecture and handed a like 100 page paper that was totally wrong)
Why haven't they explained their methods? Why is no one asking them how or what they even came up with? Why is the reporter answering all the questions and explaining? Something doesn't seem right here.
@teflontelefon it's called denial, emotion and playing on people's ignorance. They know many won't know much about the Pythagorean theorem or trig, they'll ignore the girls' arrogance ("kids don't do what we do" who says that? No humility?)and not show how they came up with their equation and many will just be happy to see 2 black girls doing something constructive.
They've presented their findings at the American Mathematical Society south-eastern (American) chapter’s semi-annual meeting in Georgia, attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech. Try to keep up.
@@keysnlemons7756 Wtf are you talking about? This is a fluff local news piece, it's not going to detail a complicated proof to idiots sitting at home. They presented at a mathematics conference. Nobody there cares about feelings, they're math nerds who care about math. The girls aren't being arrogant, they think they figured something interesting out and they wrote a paper and presented it. Why does that trigger you?
@@ShogunOfHarlem lol u mad
@@gigantomastiaCuddler lol u dumb. Mad is temporary. Dumb is forever.
Not saying they did or did not discover anything but their "findings" are not anywhere to be found outside of this 1 news broadcast and article attached. Like I want to see the math but it exists no where
@@SonofHardrada It could be ground breaking with no coverage or could be a just to try to make the school look better. either way i want to see the math
Same here, i cant find anything confirming their accuracy
If you search their names, there is a page on the AMS (American Mathematical Society) website listing the meeting where they gave their presentation. It shows the abstract, but not the paper, which I'm thinking isn't published yet.
"In the 2000 years since trigonometry was discovered it's always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.” But that isn’t quite true: in our lecture we present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry-the Law of Sines-and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1."
They didn't do it.
It's just circular reasoning.
But all kids need to win for self esteem reasons
@@MrElvis1971 so triggered.
I see a lot of haters in the comment sections. Let the experts assess the legitimacy of it when they decide to submit it to a journal.
Reminds me of that time a teenager invented his own computer.
or the clock in the suitcase
Gates Bill?
This reply reminds me of Peter Griffin, from The Family Guy.
the one that put some parts together from New Egg?
Didn't the school think it was a bomb or something?
Hi. Can someone please post a link to their detailed presentation? Thanks!
Words cannot express the powerful things I am feeling now. When you look at the video, spot near the beginning so you can see the model that was solved by a convergence function @1:30 in the video! BRILLIANT! BRILLIANT! The Black Females never to be surpassed! Everything is verified and codified!! The figure you see projected is the essence of the solution.
They won't because it's obviously fake
@@afgh1408 how is it fake?
@@afgh1408 hello guys, chill. Chill. Please don't bring ignorance to this discovery. Cluelessness is a real thing.
THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning.
Pythagorean theorem has been proven many times before. Just to let everyone know. Including using trigonometry
EXACTLY!!! What are they on?
I like how the news guy had to explain it vs the genius students explaining their own "discovery"
What are you talking about?
@@princesslovee are you illiterate?
@@princesslovee he’s pointing out that it’s kind of ridiculous they don’t let the students talk about their supposed discovery instead of watching a news guy awkwardly not explain anything about the methods
@@diverman1023 He put discovery in quotations. I think he's implying that these girls didn't discover anything.
@@pickthestickup They didn't. This is a racist propaganda piece. All of this is proven in discrete mathematics, and cross proven in algebra already, but the average scumbag is too stupid to understand what I just said so they get away with anything they want.
Ok... but... You left out the most interesting part, and provided no link to it either. (Neither does the news article in the link.)
WHERE CAN WE SEE THEIR PROOF?
Wow, A genuinely new proof of the Pythagorean Theorem! These young ladies have the gift of being able to see further and deeper than most while analyzing problems. Y'all are just the type of heroes that today's education needs. Congrats :)
what proof - the students showed no proof just a gif poiting at the sign over and over
the reporter shows lack of knowledge claiming circular logic
It's all right boo boo, you're still white😂😂😂
@@mike60521x You sound like jealous and ignorant
I think the point is not that there aren’t other proofs. It’s that they came up with a proof using trigonometry that didn’t rely on circular reasoning (ie: using the theorem to prove itself). As they say - “We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”
@schumi9xwdc this report doesn't show their findings
The Law of sines uses metric and Euclidean metric on the plane is equivalent to Pythagorean theorem.
@@visual-enthusiast
They did say that their findings will be reviewed by the larger math community beyond their local high school and teachers. Pretty sure their story will continue from there. Maybe chill, this is a great story, finally, coming from a US school (as opposed to constant school shootings in the US).
There are dozens, maybe hundreds of trigonometric proofs of the Pythagorean Theorem.
Stop hating 🤣🤣🤣🤣 it's not their fault that you stupid
You better bow before blcks.
@William Rockwell your racism is showing. Stop being disgusting.
Then why are they on the news?
@@StoicContrarian That's an easy one. Because blacks have no accomplishments of their own, so the news heralds made-up or stolen accomplishments.
I was fortunate enough to meet these young ladies and congratulate them after they received awards at the 2024 NAACP National Convention. We gave them standing ovations and delayed them for a long while taking selfies and group pictures. We are so proud!!!
Wait… they made a groundbreaking discovery, but didn’t even begin to explain how they did it? This sounds like a load of bullshit to me.
If you were mathematically literate you would see The proof is not trigonometric it is mathematic. THERE IS NO DOUBT WITH RESPECT THE VERACITY OF THESE BRILLIANT STUDENTS' ACCOMPLISHMENT! IT IS REAL! IT IS CORRECT! AND IT WAS THOUSANDS OF YEARS IN THE MAKING BY TWO YOUNG BLACK FEMALES! Words cannot express the powerful things I am feeling now.
Use your limited math skill to see that When you look at the segment beginning @1:30 in the video, You can see the model that was solved by a convergence function. The figure you see projected is the essence of the solution. BRILLIANT! BRILLIANT! The Black Females never to be surpassed! Everything is verified and codified!!
It is
They don’t just post scientific journals like its Reddit you idiot.
It has to be extensively reviewed before they officially undermine 2000 years of geniuses
I believe it has to go through a process and be confirmed first. Then it will be public, if not we’ll never hear about it again.
I really love the strong math skills, but it has been done before, a few different ways. Lazy reporting, didn’t even google? What kind of teacher asks students to do the impossible? Trig ratios like sin can be defined without Pythagorean theorem. Too bad the proof isn’t shown, but neither is even any trig! Looks like similar triangles, geometry. Unfortunately these girls are in for disappointment. There’s just so much wrong with this.
You mean they weren't working on their tik tok dances? Way to go ladies! Nice to see there are still inquisitive minds out there. Must be nice to teach your teacher. Lol
These two brilliant young women not only burst the bubble of "kids" not being able to do this work but even more so, they are young "Black" women which burst an even more contrived and ignorant myth !
Ne’Kiya Jackson copied a proof written by B. F. Yanney and J. A. Calderhead in 1896. She just turned it on its side, but other than that it is exactly the same. It can be found at a website called "cut-the-knot", Pythagorean proof 60.
Calcea Johnson copied a "geometric series" (the waffle cone) which can be found in many calculus books, which was already a proof of the Pythagorean theorem. The math used with it is a "Taylor series". She just added a triangle and called it "new", which it isn't. Also, neither is pure trigonometry like they are claiming. It's usually a homework question phrased like "find the length of the zigzag path in the triangle."
Chat GPT:
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Consider a right triangle with a right angle denoted as C. Let a and b be the lengths of the two legs and c be the length of the hypotenuse. Then:
sin C = a/c cos C = b/c
The square of the sine of angle C is:
sin^2 C = a^2 / c^2
The square of the cosine of angle C is:
cos^2 C = b^2 / c^2
Adding these two equations, we get:
sin^2 C + cos^2 C = a^2 / c^2 + b^2 / c^2 sin^2 C + cos^2 C = (a^2 + b^2) / c^2
Multiplying both sides by c^2, we get:
c^2 (sin^2 C + cos^2 C) = a^2 + b^2
Since sin^2 C + cos^2 C = 1 (because the sum of the squares of the sine and cosine of a right angle is always 1), we have:
c^2 = a^2 + b^2
This completes the proof of the Pythagorean Theorem using trigonometry.
That is circular.
@@thoreberlin Well, I will add that without it for GPT chats. I mean to check if it's their work or AI
@@zeus.9568 If it's even possible. Given that ChatGPT is bad at math and has to be hard pursuaded to get the BS out, that would also be an achievement, but of a different kind. Your readout uses sin^2+cos^2=1, which was explicitly stated to not have been used in the girls' solution in another article i read. Let's see if it makes it into Nature.
@@thoreberlin I hope that human has proven it without the help of artificial intelligence, but the basis is critical thinking. Here's another thing I'm doing with Chat, we'll see what comes out.
However, the Pythagorean theorem can also be proven using trigonometry in a different way. Let's use the law of sines for any triangle:
a/sin A = b/sin B = c/sin C
For a right triangle, the angle opposite the hypotenuse is equal to 90 degrees, so sin C = 1. Substituting this into the formula for the law of sines, we get:
a/sin A = b/sin B = c
Now divide the first expression by the second:
a/b = sin A/sin B
Using the trigonometric identity:
sin^2 A + cos^2 A = 1
We can transform it to:
sin^2 A = 1 - cos^2 A
Similarly for angle B:
sin^2 B = 1 - cos^2
This is what the video meant by circular logic 🤦♂️
I mean, really happy for them if they did it. But what's the mathematical proof?
yo cracka you aint need to see no proof.
THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning.
Lmao like you would understand it anyways
@@esotericenigmamelaninshe1253 why do you asume he wouldnt understand it?
They've presented their findings at the American Mathematical Society south-eastern (American) chapter’s semi-annual meeting in Georgia, attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech. Sorry you weren't invited.
The microaggressions from the white lady reporter are real.
When Blade said “I’ll be back”, I was flabbergasted. Truly peak cinema.
Can someone link the paper?
There IS NO paper.
There is no paper and never will be
@@LCDqBqA they are collaborating with harvard on a series of papers
@@chazlon5061 where did you hear of this
The proof was written in an ancient Egyptian language only understood by descendants of yakub
Imagine having teachers that encourage you to find new ways to solve equations. Seems like all schools usually do it wack a mole that logic down and punish you for it.😂😂. Congrats to these young ladies and bravo to the teachers for acknowledging their brilliance instead of telling them to stick to the script.
All equations were solved by the same, old methods with not a single thing new. You can't just make stuff up in math.
@@mikemondano3624 school maths then yes.. its mostly according to simplified formulas and we as students followed to a tee because they are fundamentals to advance mathematics. Math researchers will tell you otherwise that advance maths is actually VERY fluid with new discovery every few years. They just don't teach it to high school students cos it's too high level, not relevant and requires further testing at higher levels.
@@greenmatius This discussion could be unending, but I see your point. However, "discover" would be a Platonic ideal implying that math is already extant and waiting to be uncovered. New math is not created so much as derived.
I'm 100% with the news anchor in the red dress on this LMFAO XD
The square root of A squared plus b squared equals c. The reporters forgot the first part. Then they didn’t show the girls’ presentation. However they showed the anchor’s incorrect presentation.
Huh? What you said and what they showed are equivalent no? Square both sides and you get their equation
With ptolemys theorem we can proof the law of cosines. As soon as we have the law of cosines, setting gamma to be 90° gives us the pythagorean theorem
Imhotep is the father of mathematics.ptolemys were invaders.
@@berneak1 I don‘t really care. One and the same thing can have more than one name. It doesn‘t matter who was first *in that context* .
Sheeeiiitttt
Chat GPT knows it already " the Law of Sines can be used to derive the Pythagorean theorem. Here's how:
Consider a right-angled triangle with sides a, b, and c, where c is the hypotenuse (the side opposite the right angle). Let A, B, and C be the angles opposite the sides a, b, and c, respectively.
By the Law of Sines, we have:
a/sin A = b/sin B = c/sin C
Since angle C is 90 degrees, we have sin C = 1, so the third term simplifies to c.
Substituting this into the first two terms, we get:
a/sin A = b/sin B = c
Now, we can use the fact that sin^2 A + cos^2 A = 1 (the Pythagorean trig identity) to rewrite the first term:
a^2/(sin^2 A + cos^2 A) = b/sin B = c
Rearranging and substituting sin B = a/c, we get:
a^2/(c^2 - a^2) = b/c
Multiplying both sides by c^2 - a^2, we get:
a^2 = c^2 - b^2
This is the Pythagorean theorem! So we've shown that the Law of Sines can be used to derive the Pythagorean theorem without relying on the Pythagorean trig identity."
Why a/sin A = b/sin B = c/sin C ? Is it derived from Pythagorean theorem?
You've missed the point. From the abstract of their talk at an AMS meeting for undergrad research:
"In the 2000 years since trigonometry was discovered it's always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.” But that isn’t quite true: in our lecture we present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry-the Law of Sines-and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1."
@@Michelle-ym8yw so what's the point? Fi ding out something scientists already know? Btw , where is the full paper or presentation?
@@DrPhilby Ok, it looks like my reply didn't go through. Sorry if this is essentially a repost:
In mathematics, it's often less important to understand *whether* a conjecture is true, as it is to understand *why* it is true. Alternate proofs illuminate our knowledge and may point to new connections in mathematics.
As an example, the Four Color Theorem was recently proved using brute force methods that didn't really give any insight into why the theorem is true. If someone found an alternate proof that gave us some insight into the underlying mechanisms, I think a lot of people, myself included, would consider that more interesting than the first.
Alternate proofs are publishable in journals and are considered new results. Especially something as fundamental as the PT that appears throughout mathematics.
I am guessing the paper has not been published yet. I'm personally looking forward to it.
@@Michelle-ym8yw so adults with phds couldn't find it over the last centuries...and two kids have ??!! Yeah right
I feel like these news anchors could have given those young women more respect in their reporting instead of doing a whole comedy bit and wasting run time on that chalkboard "explanation" when honestly, I wanted to hear more of their proof. Just another example of people who don't understand math making low blows at people who do, because it's cool to hate math. I don't know, this whole news piece rubbed me a little wrong. Give them the time to explain things themselves instead of trying to make jokes out of it. The first guy did a good enough explanation on that piece of paper. You should have stopped it there.
yeah but then the kids would've had to show their proof and you know thats not gonna happen lol
@@BlackMasterRoshi -- Showing their proof is what the entire news segment is about.
Dude, that news anchor was happy & proud AsF that he got to show off his math skills for the first time since he's learned 'em in highschool. 😂
Being that he’s a meteorologist, he probably uses applied math to some extent daily at his job. Not like he’s falling back on that high school math, like most we’ve moved past high school
and she was like yeah, didn’t think i was ever gonna need this s*** 😂
@@bayougtr I'm well aware of the fact that we all use math in one way or another from the time we get out of bed whether we're even aware of it or not. You kinda missed my point though. I'm not really referring to how often he uses the math. I'm moreso talking about how often he gets to show those skills off.
How often do you think it is?
Would that be a daily occurrence as well?
If so, then I really wonder why he clearly seems to be so excited about it. He's obviously so proud of himself for something. I'd say that's definitely it. I've been wrong before though.
@@bayougtr Maybe you & I are just reading him, as well as the situation, quite a bit differently.
Congratulations on moving past highschool, BTW. 😁👍🤌
Every carpenter uses it every day. Even the ones with 5th grade educations who have never heard of Pythagoras and just think it's the "345 rule".
I understand how they started but would have had the students speak the entire time. Great news!!
Well good to know that you don't need to know really anything about math to work as a newscaster.
They even play that up, to make themselves relatable to an uneducated public.
Terrific story, horrible journalism. It's a *theorem*, meaning it has been proved rigorously, and has actually been so literally hundreds of different ways. These two girls seem earnest and very talented, but have not -- as the story suggests -- outpaced 2 millennia of mathematicians.
There are whole books devoted to proofs of the Pythagorean theorem that these news teams could have googled, and it's one line to show that sin^2(x) + cos^2(x) = 1 actually IS the theorem; you'd never use one to "prove" the other.
I'd love to see what the girls actually did. I'm assuming it's a fundamentally new proof, which would be awesome. But ALL mathematical proofs build on axioms (assumptions that tell us the nature of the elements we are working with, like "point" and "line") and prior proofs. This one would also need to do that to be called a "proof".
This is satire, right?
Has anyone confirmed if what these 2 girls did is accurate or not? That's a part of this story that is missing.
THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning.
It was presented at a session of the AMS for undergraduate research. You wouldn't get to present there if your results were not correct.
@@Michelle-ym8yw No. That's not how it works. Read the article in _The Guardian._
"Catherine Roberts, executive director for the American Mathematical Society, said she encouraged the St Mary’s students to see about getting their work examined by a peer-reviewed journal, even at their relatively young age.
"'Members of our community can examine their results to determine whether their proof is a correct contribution to the mathematics literature,' said Roberts, whose group hosts scientific meetings and publishes research journals."
TL;DR: Their proof has not been checked.
@@omp199 Nope. That simply means their paper hasn’t been accepted for publication yet. Their work was checked to present at a meeting of the AMS for undergraduate research. Per their website, you must submit your paper to be accepted. But in order to be accepted for publication in a journal, the argument will be gone through with a fine tooth comb, the literature will be checked to make sure this is a unique result, and the result will have to be considered significant enough for publication.
@@Michelle-ym8yw Are you serious? You are denying what I have just put in black and white right in front of your eyes.
"Members of our community can examine their results to determine whether their proof is a correct contribution to the mathematics literature," said Roberts.
Roberts is very straightforwardly implying that she doesn't know if it is correct.
Im starting to thing this is a lie to make one school better then the others💀because i check everywhere and still can't find any proof of them solving it.
THERE IS NO DOUBT WITH RESPECT THE VERACITY OF THESE BRILLIANT STUDENTS' ACCOMPLISHMENT! IT IS REAL! IT IS CORRECT! AND IT WAS THOUSANDS OF YEARS IN THE MAKING BY TWO YOUNG BLACK FEMALES! Words cannot express the powerful things I am feeling now.
When you look at the segment beginning @1:30 in the video, You can see the model that was solved by a convergence function. The figure you see projected is the essence of the solution. BRILLIANT! BRILLIANT! The Black Females never to be surpassed! Everything is verified and codified!! Thank You @Kamel for pointingn out that circular logic is NOT a proof
@@dr.michaelbatie2593 In my personal opinion, there is no actual proof of them solving the problems on the internet, just because they show a presentation of the problem does not mean they did/didn't actually solve it. Thirdly, students who go to that school should have access to the entire presentation of the equations, which can be shared with the public(this is another way for some people to believe them). There are many people who are asking for the presentation in the comments to see how they solved the problem, and not many people can find it especially me.
This is just bogus fake news. This would be earth shattering in the mathematics community and would make national news. I like how also the narrator said they proved without " trigonometry " this is contradicting what they first said. TOTAL BS
@@cocomelon2346 wow man you appreciated npc/bot account by answering that long words. But you're right about something fishy behind it
@@ditoosiahaan5077 ik its a bot i just want to get my opinion still lol
Why are you lying? Pythagoras proved it, which is why it got his name. Since then several hundreds proofs have been created. They did not use it using purely trigonometry, they also used infinite sums. Proving the theorem using *solely* trigonometry is impossible in principle.
I think news outlets should get on one page, the correct title would be "2 teens claim to have found proof using trigonometry" which apparently hasn't been done yet, mathematicians are encouraging them to submit their work for peer review. Their skin color shouldn't matter but West Africa was very fond of math and astronomy. Even if it turns out not to be true I think it's a great idea to encourage kids to pursue what they love.
I want to hear what the proof is. It sounds fascinating. The haters in the comments are giving "tell me you know nothing about math without telling me you know nothing about math". It's not about simply proving something - obviously, the Pythagorean Theorem has a number of known proofs. It's about proofs that enlighten us and show us new connections in mathematics. This one sounds like it might be intriguing. If anyone finds a writeup, let me know.
What did you hear in this news piece that makes you say it sounds fascinating? What are the "new connections" in mathematics that were even slightly alluded to here, that give ANY hint that something legitimately unique has been discovered?
@@samuelluria4744 This is from the abstract of what they presented at a session for undergraduate research at an American Mathematical Society meeting:
"In the 2000 years since trigonometry was discovered it's always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.” But that isn’t quite true: in our lecture we present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry-the Law of Sines-and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1."
@@Michelle-ym8yw - I gave you a thumbs up for going through all that trouble to type it out. I saw this, but I will look forward to seeing further publications. As far as my asking you what piqued your interest, you've gone out of your way to write out this abstract, the last line of which is the pertinent one, and I will take it that this was the answer to my question, since it was basically the only part not in the news report. Fair is fair, and I would never presume to say what should or shouldn't be of interest to anyone else. Fir me, it's very very vague. I guess we'll have to wait and see how their project progresses.
@@samuelluria4744 I just copied it from the AMS website :) I'm giving you a thumbs up too for being a good sport :)
This is relevant to my areas of research, so I guess that's why I am interested. And it's touching on some very fundamental mathematical objects which has the potential to be interesting. And since they're only in high school, it will probably involve elementary methods, which often can be very enlightening.
I'm assuming they're in the process of writing up the results, maybe getting help from a mathematician, because high school students wouldn't know how to write a professional paper. So I'm guessing that's why I can't find a paper right now. I have no idea what it will be, but yeah, my interest is piqued.
@@samuelluria4744
It is still remarkable for a couple high school students to discover a new proof for the theorem.
Only 371 have ever been found in 2000 years.
Still, it is not as groundbreaking as this news article makes it out to be
I'm not sure if using inscribed angles inside of a circle is a new thing since it's used in physics quite often...
THERE IS NO DOUBT WITH RESPECT THE VERACITY OF THESE BRILLIANT STUDENTS' ACCOMPLISHMENT! IT IS REAL! IT IS CORRECT! AND IT WAS THOUSANDS OF YEARS IN THE MAKING BY TWO YOUNG BLACK FEMALES! Words cannot express the powerful things I am feeling now.
When you look at the segment beginning @1:30 in the video, You can see the model that was solved by a convergence function. The figure you see projected is the essence of the solution. BRILLIANT! BRILLIANT! The Black Females never to be surpassed! Everything is verified and codified!!
@@dr.michaelbatie2593 bs! It's a made up story for these " queens and shiet" to feel good about yourselves
There are a lot of really simple connections between math fields that go totally ignored. There are tons of proofs and discoveries that are up for grabs (so to speak), you just have to find them.
@@dr.michaelbatie2593 you good? lmao
Brilliant job lady's
Pure genius 👏
May you go far in your studies 💐
Always nice to hear positive about our youth
Job well done 👏
RE: The 'Pythagorean' theorem:
Wikipedia: Pythagoras.
Wikipedia: Greek colonies in antiquity (c. 6th century BC).
still want to know how
But how did they prove it without circular logic and just trigonometry, show me by solving a problem.
THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning.
They did it, just not going to show how. 😂
Where/how do we watch the presentation??? I'm am so so proud of these girls!!!❤✊🏾
Why?
Because you are all so low end that basic things are some huge accomplishment?
Right.
Maybe you should watch the presentation _first,_ and _then_ be proud...?
THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning.
@Zigest Do what they've done, then speak.. Troglodyte white supremacist meme gobbler. The scum of your kind cry the hardest
News headline should read: "✊🏿 people are finally understanding math from 400 BC"
ROFLMAO. Good one.
Yet nobody explained how it's done.
In a fluff local news piece. What did you expect? Pause the video on the girls' projector slides if you want some more detail
@@BrentARJ I was checking that out. Looks like they used geometry to prove it.
Proud of you ladies!
Such a beautiful and awesome story, well deserved and achieved Calcea Johnson and Ne'Kiya Jackson 🎉
Shut up joo
@the HighPriest Except it isn’t.
The fact this isn’t being talked about shows the problem…
Has anyone fact checked this yet?
My same question
Yes. Race is verified. Gender verified
@@DrPhilby It was presented at a meeting of the AMS for undergrad research. Very well respected organization. You don't get to present there if your results are not correct. So sorry that you will never have the intellectual ability to do something like this, so you are lashing out. These girls are smarter than you. Get over it.
Yes you do, I’ve presented at one of these and there was no request as to verify what I was about to present
@@DrPhilby Another anti-woke cringelord. Go back to 2016 loser
Hmmm... "you dont see kids like us doing this." Ok. Waiting for them to show me
2 + 2= 4 who solved dis! Took da proffessas 8 years.
I'm happy these girl are interested in math, I think they have a bright future. However, the Pythagorean theorem has already been proven with literally hundreds of different methods. Are we saying it's a completely new proof? I really hate this video title/news story.
That title, tho..
Everything we've grown
accustomed to expect
from modern professional
journalism :)
"Journalism" or may I say far-left circlejerking
Mirror test for adults
Awesome job, Ladies!🎉
Congratulations for what exactly
The pythagorean theorem has been proven many times over the last 100 years! But their proof was, although it took a bit of calculus, not only trigonometry-based but also creative.
Extraordinary claim require an extraordinary evidence.
Okay let's see the proof.
Monkeys doing math is pretty extraordinary
You have to fly through the magical force field around Wakanda to see the proof.
Things like this have to be reviewed before they are published in a scientific journal.
All they have done is their submission
@@samuelluria4744 you racist salty bitch. I see all your comments about these girls you’ve made. You’re jealous because your dumbass probably hasn’t done anything of worth in your life.
THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning.
So if the teachers pushed them to uncover this 2000 year old mystery, it gives me the vibes that they already had the answer but passed the knowledge down insead
Congratulations girls!
The theorem can be proven using trigonometry if an altitude is drawn from the opposite angle to the hypotenuse, isn't this well known? what am I missing?
Finally! A sane person
Ok, so it sounds like they have a different method to prove the Law of Sines, and from there one could reverse engineer the rest of the Pythagorean theorem?
As a math-hater, what does this mean in regular terms?
The Pythagorean Theorem is a well-known result explaining the relationships of the lengths of the sides of a right triangle.
Uses for it pop up everywhere.
There are hundreds of ways to prove that the theorem is true.
These girls claim to have discovered yet another proof.
But their proof uses a field of math called trigonometry.
But trigonometry is fundamentally based on the Pythagorean Theorem.
So people are claiming that the girls are using circular reasoning: Using the Pythagorean Theorem to prove the Pythagorean Theorem.
It should be easy for someone with modest mathematical knowledge to prove who is correct.
If the girls are correct it will be front page news.
If the girls are wrong we will never hear about this again.
What I'm guessing, and what this news show isn't actually portraying is that they found a new kind of proof using trig that gives you the Pythagorean theorem as its colloraly. There are multiple proofs that are made using trig functions that subsequently arrive at Pythagorean theorem - such as Ptolomy's theorem. Where you set all your angles to π/2, that results in sin^2x + cos^2x = 1, proving the Pythagorean theorem (in this case sin is a derived function from Ptolomy's theorem, and cos is just sin moved by π/2).
so are they going to be called 'Einstein' or will Einstein will be called Calcea and Ne' Kiya?
Neither. Ne’Kiya Jackson copied a proof written by B. F. Yanney and J. A. Calderhead in 1896. She just turned it on its side, but other than that it is exactly the same. It can be found at a website called "cut-the-knot", Pythagorean proof 60.
Calcea Johnson copied a "geometric series" (the waffle cone) which can be found in many calculus books, which was already a proof of the Pythagorean theorem. The math used with it is a "Taylor series". She just added a triangle and called it "new", which it isn't. Also, neither is pure trigonometry like they are claiming. It's usually a homework question phrased like "find the length of the zigzag path in the triangle."
Great job, girls! Keep up the good work!
@the HighPriest wdym
@@-jay-2993 he's just upset that his brain is too smooth to contribute anything meaningful to world.
Since Trig is based on the pythagoras theorem, any proof of the pythagorean theorem would be using circular reasoning. there are no trigonometric proofs of the Pythagorean theorem because all of the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem. because of this theorem, we say sin2 A + cos2 A = 1 etc.
Young Black Excellence! Love it for them!!
They didn't do anything.
You are treating blacks the same way we treat retards when they are happy about the rock they found.
Stop doing that.
Dr Gabriel Oyibo have surpassed all mathematical mysteries in 1990 HE ALREADY DID THIS‼️ and this proves what he said we will start seeing this more often from “black” students
So
What’s the proof
The pre-Christian Greeks tried to understand life by philosophies that identified certain elements as the basis of all existence. Pythagoreus had many followers because he was showing that everything had a fundamental numeric element, but tradition says that he lost his followers the day that he, or a follower, applied his famous theorem to a negative triangle. Why? It was based on square roots. There is no square root for a negative number unless you multiply it by an imaginary "negative one". Suddenly, there appeared a philosophical element without a natural root, which meant the end of this "natural religion."
Ne’Kiya Jackson copied a proof written by B. F. Yanney and J. A. Calderhead in 1896. She just turned it on its side, but other than that it is exactly the same. It can be found at a website called "cut-the-knot", Pythagorean proof 60.
Calcea Johnson copied a "geometric series" (the waffle cone) which can be found in many calculus books, which was already a proof of the Pythagorean theorem. The math used with it is a "Taylor series". She just added a triangle and called it "new", which it isn't. Also, neither is pure trigonometry like they are claiming. It's usually a homework question phrased like "find the length of the zigzag path in the triangle."
Trigonometry is based on triangulation discovered in Ancient Egypt to help farmers relocate their fields after the yearly flooding of the Nile. Triangulation was done using fixed posts at the top op the hills surrounding the Nile. This is what surveyors do today unless they use global positioning satellite communication. There is a 100% chance that this new trigonometric proof will prove to be circular.
The proof is not trigonometric it is mathematic. THERE IS NO DOUBT WITH RESPECT THE VERACITY OF THESE BRILLIANT STUDENTS' ACCOMPLISHMENT! IT IS REAL! IT IS CORRECT! AND IT WAS THOUSANDS OF YEARS IN THE MAKING BY TWO YOUNG BLACK FEMALES! Words cannot express the powerful things I am feeling now.
When you look at the segment beginning @1:30 in the video, You can see the model that was solved by a convergence function. The figure you see projected is the essence of the solution. BRILLIANT! BRILLIANT! The Black Females never to be surpassed! Everything is verified and codified!!
@@dr.michaelbatie2593 THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning...... BUT... I did not see mention of the convergence function.. I was thinking they were going to resort to calculus or derivatives with the ratio of the angles and sides getting infinitely smaller. I would love to see their presentation. Many websites are just copying the same story and the reporting is very lackluster. I hope Kelsey and Nikia get help from somebody to put their presentation into a publication, this is so amazing for them, great work.
@Dr. Michael Batie
Please stop pasting copypasta.
@@dr.michaelbatie2593 Thank you for pointing this out. This is a new algebraic proof. Calcea Johnson and Ne'Kiya Jackson are great. All the other proofs still stand and we have not been waiting for 2000 years. The Pythagoras Theorem was discovered 2500 years ago in Greece, India and China and has been proven over and over by dozens of mathematicians, Euclid, Einstein even had fun coming up with the simplest and shortist proof. I do not think mathematics is about being black and/or white or non-black and/or non-white etc...Triangulation was discovered in very ancient Egypt and the first dynasties of Pharaohs were Nubian who were as black as could be.
The Generalized Theorem of Pithagora USES trigonometry so why do they say that nobody used trigonometry until now?🤨
This makes me so happy!
Well done to the two math young black girls. You have a bright future
It just bugs me when people are proud of their scientific illiteracy.
What a great story.
You can fool some of the people all of the time.
So what was their reasoning?
THE ABSTRACT FROM KELSEY AND NIKIA'S PRESENTATION: the book with the largest known collection of proofs for the theorem - Elisha Loomis’s The Pythagorean Proposition - “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem’.” ...“that isn’t quite true. We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry - the Law of Sines - and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”....... In short, they could prove the theorem using trigonometry and without resorting to circular reasoning.
They better trademark that cuz they will make a ton of money out that. What a smart and outstanding girls.
This has already been known.
And they're black ... wow... imagine that in such a superior world!
I think, there will be a bug in their proof, as such things have been checked out by billions of high-skilled mathematicians. I also had my special moments at high school sometimes, but at the end it turned out to be done before, or wrong. Anyways good luck, and good work, to have tried, thats the way it should go for your later path.
Your "special moments in high school" not withstanding, they've presented their findings at the American Mathematical Society south-eastern chapter’s semi-annual meeting in Georgia, attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech.
Unproven? No. They knew this back in ancient times.
@@leesmith2294 You can literally head up right now to google and type "Pythagoras theorem proof" and you'll see thousands of results of well established proofs of said theorem. They didn't discover anything unproven, if anything they figured out an alternative, but we don't know that because the video is vague.
@therealcatch I'm an engineer student at the top 1 engineering university of my country. I know my fair bit of mathematics and proofs, wouldn't have survived first year if I didn't.
Wonderful! Proud of you, Girls! 👩🎓👩🎓🥇🙏💯❤️✨
Where is the proof?
These 2 should be looked up to more than cardi B and Ice Spice. I hope they continue to change the world.
THE world needs more of these young ladies and less mumble rappers
End white supremacy
@@sweatygonzalez3412 End subs that moan about White anything.
@@williamrockwell9705 end caucasoids that hide behind their mobile devices..
@@sweatygonzalez3412 end the human race. we are all cringe human beings who apparently can't get along well
Love this!! proud of them!!! But let’s start with the fact that Pythagoras of Samos did not discover the theorem named after him :( The discovery of the relationship dates back to ancient Babylon, Egypt, China and Nubia. The Babylonians discovered various triples (3, 4, 5 and others using an algorithm the predates Pythagoras by over 1000 years). Good on these two brilliant young scholars but let’s start with getting the history right!!!!
these 2 black chicks doscovered nothing! garfield proved Pythagorean Theory
*discovered
@shoot4thesingle , I presume you are talking about President Garfield's proof? The one developed while he was a member of Congress? His method was interesting but geometric and not based on trigonometry...What these two young ladies may have done is utilize a ratio based proof which is similar to what we think the Babylonians used back in antiquity (predating Pythagoras of Samos by over 1000 years). Please take the time to learn these two young ladies names and not refer to them as "black chicks" (that is rude and unbecoming of a scholar as I presume you to be.) I am hoping after peer review their proof gets added to Algebra 1 and Geometry texts to inspire young folks to dig deeper...Math/Science is open to discovery if your mind is willing!!!
@@leestenson7017 look up jason zimba he proved Pythagorean Theorem with triggnomotry.
Ok, not certain why Dr Zimba is relevant to the conversation at hand. What does he have to do with these two young ladies. Presuming none of us have seen their proof so how would you know if it is similar to Dr Zimbas or not???? Be patient and wait for the peer review and we all can see the proof they completed and whether it is a new proof or similar to something that has already been done…I still stand behind how proud I am of these very bright young ladies…They are destined for great things!!!! Please try to be more encouraging of youth vs going into attack mode and certainly respect people of all nationalities and ethnicities…That is just common decency!!!
The incels and racists never fail to show up in the comments.
Someone explain using NBA logic ….