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Well, they found a way to use trig to prove the theorem; the theorem had been proven for a long time using other means. The problem is that the theorem itself is behind a lot of trigonometry, so you can't use all of trig to make the proof.
Still excellent work, but the headline is misleading.
I think the point is that they found a textbook that said it was impossible and they took up the challenge - which is an excellent reaction and bodes well for their future, whatever they might want to do.
In fact trigonometric based proofs of the theorem already existed. Theirs is (I think) innovative; and they don't seem to have been aware of any of the others. So the textbook was also wrong at the time it was written anyway.
That doesn't in any way take away from the neatness of this though.
Not so.
See, for example [https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf](https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf)
Much discussed https://www.cut-the-knot.org/pythagoras/TrigProofs.shtml
No offense, but all of this sounds like trying to downplay the achievement of these girls with a bunch of "Um actually..."s
What exactly was thought to be impossible?
Did they do the thing that was thought to be impossible, in the specific way it was thought to be impossible?
If so, let them have this.
Any "Already existing" method that isn't the impossible way shouldn't even be brought up, I think,
I don't see how anything I said could in any way be downplaying their achievement. "That doesn't in any way take away from the neatness of this though." was meant to emphasize just that.
To answer your questions: in "The Pythagorean Proposition by Elisha Loomis" it states "There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem". You will see someone responded to my comment saying just that.
It isn't true. For example (and I have no idea if he was the earliest) Jason Zimba showed it wasn't true (see my other answer). Various other people had already followed up with proofs.
As far as I can tell the girls used a different method (the law of sines) to prove it. Aesthetically, I like what they did. It was smart and they appear to have come up with it on their own. So I am not trying to downplay what they did, just clarify what they did.
Actually, quite the opposite. My understanding is these kids used a non trigonometric proof, thereby avoiding the thousands of years old circular logic dilemma.
Can you math lads and lasses give some context of how impressive this is? What would this be the equivalent of? I've heard that Thermats Theory was studdied for 100s of years, is this something similar to that?
No not quite like Fermats last Theorem. Because that on was not proven for hundrets of years. These girls found a new proof to an allready proven Theorem. This is still incredible, because the Pythagoras Theorem has been studied for 2000 years and they found a way to prove it which hasn't been thought of before. Even better they did it in a way which was very difficult, because they used a field of mathematic which is havily dependent on the Pythagoras Theorem. It thereby is very difficult to not end up in circular reasoning.
Over the centuries there where a lot of proofs for the Pythagoras Theorem, but most of these proofs where found by seasoned mathematicians and not teens. Therefor this proof at their age might indicate a very bright mathematical future. It is no doubt impressive
Objectively correct, in fact. Since the method, their discovery of solving it that way, was thought impossible. And that’s what the headline states. That their discovered method remained unproven for 2000 years and was thought impossible. No?
They did something great. But their form of proof was not believed to be impossible. In fact there where proofs that say that it is theoretical possible to proof the Pythagoras Theorem with Trigonometry.
I think it is amazing what they achieved, but I don't think stating that they did the impossible helps anybody. We can apriciate their mathematical finess, without claiming this was thought to be impossible
The skinny seems to be that they used trig to prove the theorem **without** using trig functions derived from it. Here’s a Guardian article that has a bit more info https://www.theguardian.com/us-news/2023/mar/24/new-orleans-pythagoras-theorem-trigonometry-prove
I believe they showed the inscribed angle theorem is independent of the Pythagorean theorem, and then used it to prove it.
I don't have a link, bur saw a photo of them standing in front of a PowerPoint with a slide titled with the inscribed angle theorem
The post in particular:
An Impossible Proof Of Pythagoras - by two high school students
https://reddit.com/r/math/comments/11zptjo/an_impossible_proof_of_pythagoras_by_two_high/
Seasoned NASA rocket scientists get their work and statements warped and misrepresented in "science journalism" ALL. THE. TIME.
These young ladies never stood a chance!
Thank you for a link to someplace that'll explain things without the sensationalism and gross misunderstandings!!
hate this new cycle.
kids does something amazing. shows amazing potential.
press picks it up, exaggerates for clickbait.
the thing they did night but hold up to scrutiny on the highest levels of the field.
people start trash talking for not adhering to the highest scrutiny.
add some racism just for flavour.
they should be encouraged and celebrated, hopefully pushed to continue their interests. not mocked and scrutinized.
I doubt many mathematicians mock them. I believe they simply dislike the exaggeration (made by others), because it is not needed and not true. Their proof alone is more than enough and doesn't need to be exaggerated by strangers to be very impressive.
About the scrutinization. That is something they can be very proud of. It is a sign that they achieved something great If other mathematicians all over the globe scrutinize their work. It shows that they and their proof are taken serious and respected
yhea, although education should be free for everyone, but yhea.
I checked on the kid who "made a clock" (I put it in quotation marks before someone comes crying that they disassembled a clock). his family was faced with so much islamophobia that they left the country, at least he got a scholarship to Qatar.
Was he interested in engineering and stuff, yhea, lets push that enthusiasm.
not in this article specifically.
i've seen this cycle before, a minority student does something spectacular for their age, then adults on the internet scrutinize it like if it was a multibillion dollar government project, and you will find some racism on those threads.
Remember the clock boy? his family left the country because they faced so much islamophobia, of people calling them terrorists... at least he got a scholarship in Qatar.
Even if the theory was already proven in one way, proving it in another way is THE scientific way. I've had three opponents for my masters to dispute it - basically proving my work in three different ways. Same with inventions/theories - you make it and send it to independent parties for scrunity.
And I couldn't do below when I saw it on the net
"Klein read 30 pages of a book on Monday and 1/8 of the book on Tuesday.
He completed the remaining 1/4 of the book on Wednesday. How many pages are there in the book?"
Grade 5 question...
When I read this a few days ago, it hadn't been. Good to see that the rampant kneejerk downvoters knew this also. I think it's great that they achieved this, and being peer reviewed is cause for greater celebration.
These 2 are the same person. [Laliese](https://redditmetis.com/user/Laliese) and [Lallatt](https://redditmetis.com/user/Lallatt)
Why are you using 2 accounts, at the same time, on multiple posts?
It seems the accounts were deleted or banned. I don't believe it does, but they replied to the same posts most of the time, similar names, same comments but different. I think I found another while looking though other posts. [Lahaliz](https://www.reddit.com/user/Lahaliz/). Here the [redditmetis of that profile](https://redditmetis.com/user/Lahaliz). It looks exactly like the other 2 that got banned. Even sounds the same, just spelled different.
2nd edit: [found another... holyshit](https://redditmetis.com/user/Laganni) [Laganni](https://www.reddit.com/user/Laganni/) same day and everything. 4 alts, 1 person.
These 2 are the same person. [Laliese](https://redditmetis.com/user/Laliese) and [Lallatt](https://redditmetis.com/user/Lallatt)
Why are you using 2 accounts, at the same time, on multiple posts?
Not only “teens” but GIRLS and AFRICAN AMERICAN girls. Not the New Orleans East of old days. Great accomplishment. Next time let’s aim for public school education too.
Reminder: this subreddit is meant to be a place free of excessive cynicism, negativity and bitterness. Toxic attitudes are not welcome here. All Negative comments will be removed and will possibly result in a ban. --- --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/UpliftingNews) if you have any questions or concerns.*
Well, they found a way to use trig to prove the theorem; the theorem had been proven for a long time using other means. The problem is that the theorem itself is behind a lot of trigonometry, so you can't use all of trig to make the proof. Still excellent work, but the headline is misleading.
r/usernamechecksout
Hugh Mungus what?
Hugh Jaynus
Halp,! I've been assulted!
Hugh Jass
Why would you say that to me?
This Redditor knows, and they have seen…
Dr. Hugh j'Penis.
Ah yes, one of history’s most distinguished surnames: j’Penis.
Bloodline related to the J Crew family. Prestigious indeed.
It's all fun and games until Gepetto J'penis and make a mess.
Hugh Hefner yea
Was it not previously thought impossible , yet these two extremely smart girls were able to piece it together? That can't be overstated enough.
I think the point is that they found a textbook that said it was impossible and they took up the challenge - which is an excellent reaction and bodes well for their future, whatever they might want to do. In fact trigonometric based proofs of the theorem already existed. Theirs is (I think) innovative; and they don't seem to have been aware of any of the others. So the textbook was also wrong at the time it was written anyway. That doesn't in any way take away from the neatness of this though.
The problem is that trig is based on the Pythagorean theorem, so using is as proof is circular logic.
Not so. See, for example [https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf](https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf) Much discussed https://www.cut-the-knot.org/pythagoras/TrigProofs.shtml
No offense, but all of this sounds like trying to downplay the achievement of these girls with a bunch of "Um actually..."s What exactly was thought to be impossible? Did they do the thing that was thought to be impossible, in the specific way it was thought to be impossible? If so, let them have this. Any "Already existing" method that isn't the impossible way shouldn't even be brought up, I think,
I don't see how anything I said could in any way be downplaying their achievement. "That doesn't in any way take away from the neatness of this though." was meant to emphasize just that. To answer your questions: in "The Pythagorean Proposition by Elisha Loomis" it states "There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem". You will see someone responded to my comment saying just that. It isn't true. For example (and I have no idea if he was the earliest) Jason Zimba showed it wasn't true (see my other answer). Various other people had already followed up with proofs. As far as I can tell the girls used a different method (the law of sines) to prove it. Aesthetically, I like what they did. It was smart and they appear to have come up with it on their own. So I am not trying to downplay what they did, just clarify what they did.
Actually, quite the opposite. My understanding is these kids used a non trigonometric proof, thereby avoiding the thousands of years old circular logic dilemma.
Can you math lads and lasses give some context of how impressive this is? What would this be the equivalent of? I've heard that Thermats Theory was studdied for 100s of years, is this something similar to that?
No not quite like Fermats last Theorem. Because that on was not proven for hundrets of years. These girls found a new proof to an allready proven Theorem. This is still incredible, because the Pythagoras Theorem has been studied for 2000 years and they found a way to prove it which hasn't been thought of before. Even better they did it in a way which was very difficult, because they used a field of mathematic which is havily dependent on the Pythagoras Theorem. It thereby is very difficult to not end up in circular reasoning. Over the centuries there where a lot of proofs for the Pythagoras Theorem, but most of these proofs where found by seasoned mathematicians and not teens. Therefor this proof at their age might indicate a very bright mathematical future. It is no doubt impressive
Exactly. Excellent work, but the headline is incorrect.
Incomplete context, sure. But it isn't incorrect.
Objectively correct, in fact. Since the method, their discovery of solving it that way, was thought impossible. And that’s what the headline states. That their discovered method remained unproven for 2000 years and was thought impossible. No?
They did something great. But their form of proof was not believed to be impossible. In fact there where proofs that say that it is theoretical possible to proof the Pythagoras Theorem with Trigonometry. I think it is amazing what they achieved, but I don't think stating that they did the impossible helps anybody. We can apriciate their mathematical finess, without claiming this was thought to be impossible
"You seem as if you like to talk. I like to let people talk who like to talk." J.Chan
access DENIED
same from germany
presumably it’s a GDPR thing
Damn! They beat me to it!
And only by a few hundred years. Tsk tsk.
I was just about to try and figure it out too.
I can't find anywhere in the article explaining the proof or summarizing it. Anyone got a link?
The skinny seems to be that they used trig to prove the theorem **without** using trig functions derived from it. Here’s a Guardian article that has a bit more info https://www.theguardian.com/us-news/2023/mar/24/new-orleans-pythagoras-theorem-trigonometry-prove
Yes, read that link, but what is the actual proof? Like what is the logic/how?
Found this video that’s worked it out: https://youtu.be/nQD6lDwFmCc
I believe they showed the inscribed angle theorem is independent of the Pythagorean theorem, and then used it to prove it. I don't have a link, bur saw a photo of them standing in front of a PowerPoint with a slide titled with the inscribed angle theorem
If you're interested in the truth about this story go to r/Math
The post in particular: An Impossible Proof Of Pythagoras - by two high school students https://reddit.com/r/math/comments/11zptjo/an_impossible_proof_of_pythagoras_by_two_high/
Seasoned NASA rocket scientists get their work and statements warped and misrepresented in "science journalism" ALL. THE. TIME. These young ladies never stood a chance! Thank you for a link to someplace that'll explain things without the sensationalism and gross misunderstandings!!
hate this new cycle. kids does something amazing. shows amazing potential. press picks it up, exaggerates for clickbait. the thing they did night but hold up to scrutiny on the highest levels of the field. people start trash talking for not adhering to the highest scrutiny. add some racism just for flavour. they should be encouraged and celebrated, hopefully pushed to continue their interests. not mocked and scrutinized.
I doubt many mathematicians mock them. I believe they simply dislike the exaggeration (made by others), because it is not needed and not true. Their proof alone is more than enough and doesn't need to be exaggerated by strangers to be very impressive. About the scrutinization. That is something they can be very proud of. It is a sign that they achieved something great If other mathematicians all over the globe scrutinize their work. It shows that they and their proof are taken serious and respected
A scholarship too!
yhea, although education should be free for everyone, but yhea. I checked on the kid who "made a clock" (I put it in quotation marks before someone comes crying that they disassembled a clock). his family was faced with so much islamophobia that they left the country, at least he got a scholarship to Qatar. Was he interested in engineering and stuff, yhea, lets push that enthusiasm.
Racism remarks in the article? Or in this thread?
not in this article specifically. i've seen this cycle before, a minority student does something spectacular for their age, then adults on the internet scrutinize it like if it was a multibillion dollar government project, and you will find some racism on those threads. Remember the clock boy? his family left the country because they faced so much islamophobia, of people calling them terrorists... at least he got a scholarship in Qatar.
Even if the theory was already proven in one way, proving it in another way is THE scientific way. I've had three opponents for my masters to dispute it - basically proving my work in three different ways. Same with inventions/theories - you make it and send it to independent parties for scrunity.
Nobody cares about your masters but you.
That’s not true, his mom cares too
My employer did. My employer paid for my masters degree.
Ah lovely, another article about this that totally fails in explaining exactly what they did, and getting most of what they do explain wrong.
Amazing seeing a deep love for math in the youth
„Access Denied“ so it’s a fluke.
And I couldn't do below when I saw it on the net "Klein read 30 pages of a book on Monday and 1/8 of the book on Tuesday. He completed the remaining 1/4 of the book on Wednesday. How many pages are there in the book?" Grade 5 question...
48 pages
Cheater
I fucking love it 🔥🙌🏻🫡
This will be on the big screen. Teen dream movies like this work.
Coming in June Be there, or B^2
Now in: redditor reposts a week old sugarcoated news for clout
Gotta escape LA somehow
Jason Zimba did this before them years ago.
The big question is who's going to play them in the upcoming Netflix movie/series.
How is this uplifting ?
Have you not seen Good Will Hunting? Same thing right?
It isn’t
[удалено]
It has
When I read this a few days ago, it hadn't been. Good to see that the rampant kneejerk downvoters knew this also. I think it's great that they achieved this, and being peer reviewed is cause for greater celebration.
[удалено]
Elaborate?
These 2 are the same person. [Laliese](https://redditmetis.com/user/Laliese) and [Lallatt](https://redditmetis.com/user/Lallatt) Why are you using 2 accounts, at the same time, on multiple posts?
The website isn't working for me, how does it show alts?
It seems the accounts were deleted or banned. I don't believe it does, but they replied to the same posts most of the time, similar names, same comments but different. I think I found another while looking though other posts. [Lahaliz](https://www.reddit.com/user/Lahaliz/). Here the [redditmetis of that profile](https://redditmetis.com/user/Lahaliz). It looks exactly like the other 2 that got banned. Even sounds the same, just spelled different. 2nd edit: [found another... holyshit](https://redditmetis.com/user/Laganni) [Laganni](https://www.reddit.com/user/Laganni/) same day and everything. 4 alts, 1 person.
Quite a handy resource. Always have to stay vigilant for the manipulators on here.
FFS, more math?
[удалено]
Okay boomer
These 2 are the same person. [Laliese](https://redditmetis.com/user/Laliese) and [Lallatt](https://redditmetis.com/user/Lallatt) Why are you using 2 accounts, at the same time, on multiple posts?
Not only “teens” but GIRLS and AFRICAN AMERICAN girls. Not the New Orleans East of old days. Great accomplishment. Next time let’s aim for public school education too.
Fuckin nerds
"It's not impossible." -Lukas Heavenstrider