131–140 of 287 posts
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…
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Well sure, there are other proofs of Pythagorean theorem. The interesting part is that this is a new proof.
I'm certainly no expert on proofs of the Pythagorean theorem, but if their construction is novel, then the above may be too.
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> This is the Louisiana education system in the USA, a state which is rather notorious for having sub-par education What does this have to do with anything? Exceptional people come from absolutely anywhere, and seek to learn on their own. It's as true in Louisiana as it is in Massachusetts. Ken Thompson was born and (at least partly, afaik) raised in Louisiana, for example. Are we all just dumb people using a dumb pe…
There’s even people from the state that read this forum now and then
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Perhaps the website for the school is incomplete and only listing registration fees and not tuition but the only figure I see is $750, which is not nothing for plenty of families but is hardly what I would call expensive when it comes to private education. Am I missing something? Very well could be!
Parents that care are a huge predictor of academic success. Putting your child in a private school, even an affordable one, is more effort than just going with the default option and thus serves as signal for parents caring.
I don't like how the author drops the bomb "this has been done before" and tries to compensate that with the "simple and lively" language of the proof, or the background of the girls.
Why didn't author reference any of the previous work? How do they differ from Jackson and Johnson's proof? What's the novelty here? How can we properly give credit to these young mathematicians?
> 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.
The article's author is very clear whose ideas they are reporting. Neither do they aspire to be the definitive citation for the idea. They hope the girls publish, or attempt to publish, and in the process establish their priority by peer review. This is perfectly legit in academic publishing. Credit where credit is due is the rule. You are not obliged to keep stuff secret until the originator has published, only that…
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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…
Nearly all the nontrivial results of trigonometry do in fact rest on the pythagorean theorem. The trig identities you learned in high school, as well as more advanced results like power series, etc. These results would be inadmissible.
So the “uses trigonometry” part of this story feels like an attempt to manufacture mystery and hype. Which is a shame, because the geometric series construction is imo the interesting part, and can stand on its own merits.
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.
No. There are true statements which cannot be proven. For example: "This statement cannot be proven." (Technically it's truth value is neither true nor false. It is an imaginary Boolean value.)
how does one define sin without Pythagorean theorem? E. g. need to prove that it only depends on angle and not triangle size.