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New Orleans teenagers found a new proof of the Pythagorean Theorem

keith-mcnulty.medium.com

111–120 of 287 posts

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

#111

> By all accounts, these two teenage math students are the exact opposite of the majority of the math establishment. They are female, they are African-American, and they come from an area which is not particularly renowned for producing high academic achievers. This is just an awesome turn of events and one which should inspire anyone — no matter what their ethnic, gender or socio-demographic background — that excell…

I think it's just fucked up these things needs to be mentioned at all.

We're all fucking humans. Great job to these persons*

* = a human being regarded as an individual

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

#112

I don't get how this is "new" or "novel" ? it seems to me the law of cosine (or al kashi's theorem) we study this in high school in France ... https://en.wikipedia.org/wiki/Law_of_cosines

It's the Pythagorean theorem, a special case of the law of cosines. What's new is the proof method.

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

#113

> By all accounts, these two teenage math students are the exact opposite of the majority of the math establishment. They are female, they are African-American, and they come from an area which is not particularly renowned for producing high academic achievers. This is just an awesome turn of events and one which should inspire anyone — no matter what their ethnic, gender or socio-demographic background — that excell…

I think it's just fucked up these things needs to be mentioned at all. We're all fucking humans. Great job to these persons* * = a human being regarded as an individual

That's what centuries of oppression does. It makes this rare. Hopefully, elevating these achievements in the community can make a difference. Ignoring that this problem exists certainly won't. If you don't care about broadening the pool of mathematicians, simply ignore the part of the article about that subject.

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

#114

[flagged]

> When I read "New Orleans teenagers" I wanted to immediately give the benefit of the doubt, but a part of me suspected they may lead with identity.

I didn’t have this reflexive reaction, but I can understand why one might if familiar with the way regional references can be coded language. That said,

> It does a disservice to an achievement, if in fact there is one. A part of me is now sort of doubtful that this isn't a "cause celebre" sort of situation.

I don’t think it does a disservice. The author isn’t noting the achievement because of the students’ identity, only noting that the objective achievement being achieved by students with systemic disadvantages might be inspiring to others facing similar disadvantages. As an educator, one of their responsibilities is to help students overcome arbitrary barriers to their education and enjoy the benefits of the same education as their peers. It’s one of zillions of implied responsibilities educators have beyond the material itself. But you can’t fault any educator for recognizing when one factor of that might be even a little less fraught by centuries of reinforced barriers to their students.

The rest of the paragraph you quoted seems to reflect your own view:

> which should inspire anyone — no matter what their ethnic, gender or socio-demographic background — that excellence in your chosen field of study is always attainable if you have enough joy and passion for what you do.

The difference is that the author seems to recognize that wishing doesn’t make it so, that systemic and historical barriers don’t vanish if you don’t mention them.

The rest of the post is focused on the objective details. I hope that won’t be lost because you or anyone is sensitive to acknowledgment that humans don’t exist in a vacuum even if you that for the math they’re reasoning about.

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

#115

Earlier quoted context omitted.

I think it's just fucked up these things needs to be mentioned at all. We're all fucking humans. Great job to these persons* * = a human being regarded as an individual

That's what centuries of oppression does. It makes this rare. Hopefully, elevating these achievements in the community can make a difference. Ignoring that this problem exists certainly won't. If you don't care about broadening the pool of mathematicians, simply ignore the part of the article about that subject.

[deleted]

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

#116
post #99

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.…

[deleted]

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

#119

Ok, I read through the proof, and I think I understood it. Thanks for posting this! Until the authors' work is submitted to a journal and reviewed, it's hard to say everything claimed here is definitely correct & new. Update: Nice video on the proof: https://www.youtube.com/watch?v=nQD6lDwFmCc I like what they did :) Seems legit to me. Btw, law of sines can be proven independently of pythagoras. So using that as a st…

It's obviously correct (it's basic high school math; as with most proofs, the cleverness is in the construction, not the computation) and nearly obviously new or at least newly published. (There are many easily searchable collections of proof, but not everyone published their proof of a theorem already proved and published over 400 different ways)

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

#120

for completeness, here is a reference to the AMS presentation. https://meetings.ams.org/math/spring2023se/meetingapp.cgi/Pa... [my post updated to include abstract] Abstract 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 Pythag…

Note that in math "flatly" means "asserted without proof", not "incontrovertible".

"Trigonometry" is not formally defined, so Loomis's statement is merely tautological.

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