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New Orleans teenagers found a new proof of the Pythagorean Theorem

keith-mcnulty.medium.com

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Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#121

Post by hgsgm »

agurjal wrote: post #89

I think you can sidestep trigonometry (and the Law of Sines) completely. You can decompose any triangle A, B, C using their construction to create smaller triangle a, b, c where A = 2abc/(b² - a²), C = c(b² + a²)/(b² - a²), and B = c. This can be shown with only similar triangles (it seems like they unnecessarily use sines in the article). It is then just algebra to show A² + B² = c²(b² + a²)²/(b² - a²)² = C². edit:…

The Law of Sines is proven using similar triangles. This is a convenient way to bookkeep similar triangles.

Does your version using the infinite series, or only the waffle cone shape?

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#122

Post by hgsgm »

yosito wrote: post #87

> doing my best to explain how Johnson and Jackson proved it using simple trigonometry. Although their proof hasn’t been published They didn't publish it, but this author is just going to take the liberty to publish their work himself? If I were one of these teenagers, this would make me angry.

They already presented it at conference. If they are angry (they aren't), it would be their own fault for rushing to the ignorant media for fake publicity before publishing to the math community. Already we see that their approach led to massive fake news reporting based on journalists who had no experts to explain what actually happened, and relied on unvetted claims by high school students (not totally their fault) and their school admins (their fault).

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#123

Post by hgsgm »

maxk42 wrote: post #75

On my phone at a restaurant right now so I'm not looking it up but this was previously in a published paper in 2009. Not to rain on their parade: this is a great start for a couple of math prodigies, but they didn't quite discover a new proof.

No, that was a different proof using different trigonometry.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#125

Post by criloz2 »

rvz wrote: post #97

Well deserved and well done to them on this proof. It is quite interesting to see that the AI bros continue to hype and worship hallucinating sophists like ChatGPT and GPT 4. By now we should have already expected that AIs like LLMs are able to create unique proofs and new solutions to existing unsolved mathematical problems. They still haven't after years of hype and not even one single mention of buzzwords like 'LL…

Why are being downvoted?, there have been crazy comment on this website, hyping to the max ChatGPT and how all the humans now are useless, I was just ignoring HN for the past weeks because it have been ridiculous

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#126

Post by eyelidlessness »

pedrosorio wrote: post #37
JKCalhoun wrote: post #27

Earlier quoted context omitted.

That's not the way I took the article. Rather I took it to mean something slightly different: Your ethnicity and/or gender should not be seen as a barrier to advanced mathematics. There is a nuanced difference there.

I would also take that interpretation if the author didn't explicitly mention "socio-demographic background". They should just leave that one out next time.

> > Your ethnicity and/or gender should not be seen as a barrier to advanced mathematics.

> I would also take that interpretation if the author didn't explicitly mention "socio-demographic background". They should just leave that one out next time.

Please help me understand. Are you saying that it’s okay to say that ethnicity and/or gender should not be seen as a barrier to advanced mathematics, so long as you don’t explicitly acknowledge that ethnicity and/or gender may presently be a barrier to advanced mathematics?

How does that even work? We achieve a meritocracy inherently based on not mentioning that we don’t have anything resembling a meritocracy? Because identifying reality is what makes it real?

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#127

Post by coliveira »

dendrite9 wrote: post #49

I remember reading a book in high school and realizing there could be other ways to prove things that I had been taught only one way. One that particularly stood out later was using a rotating fishtank to prove the pythagorean theorum. A good friend of mine was so delighted by the example I gave him a copy of the book I found it in. https://press.princeton.edu/books/paperback/9780691154565/th... ) The relevant sectio…

The nice thing about mathematics is that for every true statement there are infinitely many proofs. Granted, some are just variations of others, but there many ways to reach the same point.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#128

Post by eyelidlessness »

malshe wrote: post #2

The actual title is "Here’s How Two New Orleans Teenagers Found a New Proof of the Pythagorean Theorem" but I don't know why HN automatically converted it to this title.

I share your dislike for this title editing, and agree the original title is better.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#129

Post by steppi »

dendrite9 wrote: post #49

I remember reading a book in high school and realizing there could be other ways to prove things that I had been taught only one way. One that particularly stood out later was using a rotating fishtank to prove the pythagorean theorum. A good friend of mine was so delighted by the example I gave him a copy of the book I found it in. https://press.princeton.edu/books/paperback/9780691154565/th... ) The relevant sectio…

This is a really great book. It’s very accessible but the insights can also be appreciated by a mathematically sophisticated audience. I’m particularly fond of Chapter 11 on understanding complex analytic functions and the part in Chapter 2 that gives a very clear explanation why the determinant formula gives the (signed) volume of the parallelepiped determined by the column vectors of a matrix.

Re: New Orleans teenagers found a new proof of the Pythagorean Theorem

#130

Post by fnordpiglet »

jonahx wrote: post #99
joe_the_user wrote: post #20

I have read about this proof for a bit and this is the first write-up that gives the slightest details. The phrase "using trigonometry" is confusing. What they do is assume functions sine and cosine exist, as normally defined, as ratios of triangle values, without assuming these have the various Pythagorean-theorem derived properties. They then construct an infinite series of nested triangles and use the formula for…

It's a very clever proof. Agreed "using trigonometry" is potentially misleading. After reading the proof, the only 2 senses in which "trignometry" is being used are: 1. The term "sin a" is used to denote the ratio opposite / hypotenuse. But this can be considered a purely notational convenience. They could have called it "foo a" and nothing would change, or they could have inlined the referred-to ratio everywhere. 2.…

Is there more to trigonometry? I’m not a abstract math person, so forgive the ignorance, but my understanding was all trigonometric functions derive from ratios of angles and lengths of triangles so in the end each occurrence of a trigonometric function can be replaced by the corresponding ratios in some triangle. There are other ways to construct things, such as power series representations, etc, but even these must necessarily be replaceable by the ratio of angles and lengths of some triangle. What am I missing?
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