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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

#271

Post by dvt »

chx wrote: post #201
dvt wrote: post #179

Earlier quoted context omitted.

This is super cool, I've never seen it before! Do you know what this is called so I can look up a proof/theorem on it?

I asked https://math.stackexchange.com/q/124887/6400 I wish I had a more modern summary of the papers mentioned in the linked paper > Tannery, Fonctions d'une Variable, 1886, p. 147. Osgood, Lehrbueh der Funktionentheorie, 1912, p. 582. Van Vleck and H'Doubler, Transactions Amer. Math. Society, vol. 17 (1916), p. 30 because we spent an entire semester at the university in one class working on these two.

> because we spent an entire semester at the university in one class working on these two.

Yeah, the Math Overflow answers are a bit sparse, and I think the Euler formulation (while clever) is a bit of a red herring and might be circular. Trying to slowly go through that 1917 paper, thanks for linking!

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

#272

Post by pedrosorio »

eyelidlessness wrote: post #163
pedrosorio wrote: post #157

Earlier quoted context omitted.

Read the thread I am responding to.

I did.

Cool. The summary then is:

Ethnicity and Gender and Socio-demographic background != Ethnicity and Gender

What you asked in your first comment seem to be orthogonal to the point I was making.

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

#273

Post by iamerroragent »

cabalamat wrote: post #228
iamerroragent wrote: post #212

Earlier quoted context omitted.

I disagree. 'Aesthetic' appearance in math is important in helping drive mathematical innovation and help new human beings derive pleasure from that wonderful field. Programming is kind of an applied mathematics where efficiency does matter because it's a tool, a means to an end. Not to say that people can't find aesthetics in programming, nor that they shouldn't, rather in math at least the pleasure of discovering a…

I find simplicity aesthetically appealing. Obviously some other people differ.

Well you're in luck since these girls' proof is pretty simple so should be pretty pleasing for you!

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

#274

Post by eyelidlessness »

pedrosorio wrote: post #272
eyelidlessness wrote: post #163

Earlier quoted context omitted.

I did.

Cool. The summary then is: Ethnicity and Gender and Socio-demographic background != Ethnicity and Gender What you asked in your first comment seem to be orthogonal to the point I was making.

Ethnicity and gender are two socio-demographic factors of many, yeah. So if I’m understanding you, it’s okay for the educator to want students to feel encouraged to succeed regardless of their ethnicity and gender, but shouldn’t mention any other socio-demographic barriers they might overcome? Or should specify them all? I’m trying to understand why mentioning the term is objectionable.

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

#275

Post by pedrosorio »

eyelidlessness wrote: post #274
pedrosorio wrote: post #272

Earlier quoted context omitted.

Cool. The summary then is: Ethnicity and Gender and Socio-demographic background != Ethnicity and Gender What you asked in your first comment seem to be orthogonal to the point I was making.

Ethnicity and gender are two socio-demographic factors of many, yeah. So if I’m understanding you, it’s okay for the educator to want students to feel encouraged to succeed regardless of their ethnicity and gender, but shouldn’t mention any other socio-demographic barriers they might overcome? Or should specify them all? I’m trying to understand why mentioning the term is objectionable.

Mentioning ethnicity, gender AND socio-demographic factors, implies this case is a good illustration of OTHER socio-demographic factors that have to be overcome in order to succeed.

In particular, with no further information, one might assume a lot more about the difficulties these two girls had to overcome being African American in Louisiana. The State's public schools famously rank very poorly, and there is a strong correlation between socio-economic reality and ethnicity.

That's why a comment upthread quoted that section of the article and mentioned it is remiss not to mention the two girls attended a private Catholic school with ~$10k/year tuition.

Further down the thread, someone says the message they got from the article was how ethnicity and/or gender should not be seen as a barrier to advanced mathematics.

I disagreed that is the only thing the article says. The article does mention this as an inspiring case for people who may see themselves excluded from advanced mathematics because of gender/ethnicity AND other socio-demographic factors. Some very important ones that hold back a lot of black girls (and boys) in the US do not apply in this case.

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

#276

Post by eyelidlessness »

pedrosorio wrote: post #275
eyelidlessness wrote: post #274

Earlier quoted context omitted.

Ethnicity and gender are two socio-demographic factors of many, yeah. So if I’m understanding you, it’s okay for the educator to want students to feel encouraged to succeed regardless of their ethnicity and gender, but shouldn’t mention any other socio-demographic barriers they might overcome? Or should specify them all? I’m trying to understand why mentioning the term is objectionable.

Mentioning ethnicity, gender AND socio-demographic factors, implies this case is a good illustration of OTHER socio-demographic factors that have to be overcome in order to succeed. In particular, with no further information, one might assume a lot more about the difficulties these two girls had to overcome being African American in Louisiana. The State's public schools famously rank very poorly, and there is a stron…

So your problem is that these individual students weren’t oppressed enough to warrant an educator’s broader generalization that all students shouldn’t be held back by their many and varied forms of barriers?

If you recognize that there’s a vast set of intersecting disadvantages, why would you want to turn it into Oppression Olympics? It’s fine to recognize that not all of those power dynamics might be in play in this particular case. But do they really have to all be in play to make a fairly bland statement that no one should be held back by any of them?

I have solidarity with these students just as I have with others who have different socio-demographic factors to contend with. They’re not and shouldn’t be in competition for access to education or achievement in life. I don’t understand why that should be controversial even if each and every student has a different configuration of advantages and disadvantages. And I think it does a disservice to the students who have different disadvantages to say no one should speak about them in a unifying way unless they meet an exacting criteria of total disadvantage.

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

#277

Post by chx »

dvt wrote: post #179
chx wrote: post #151

Earlier quoted context omitted.

You can define sine and cosine together using the functional equations S(X)C(Y)+C(X)S(Y)=S(X+Y) C(X)C(Y)−S(X)S(Y)=C(X+Y) The only solutions to this are the constant 0 functions and the sine-cosine pair.

This is super cool, I've never seen it before! Do you know what this is called so I can look up a proof/theorem on it?

Also related: doi:10.1007/s00010-003-2700-z

f(x)f(y)f(z) = f(x) + f(y) + f(z) sort of implies f(x) is tan(x) -- it's actually tan(kx + (1-k) pi/3).

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

#278

Post by pedrosorio »

eyelidlessness wrote: post #276
pedrosorio wrote: post #275

Earlier quoted context omitted.

Mentioning ethnicity, gender AND socio-demographic factors, implies this case is a good illustration of OTHER socio-demographic factors that have to be overcome in order to succeed. In particular, with no further information, one might assume a lot more about the difficulties these two girls had to overcome being African American in Louisiana. The State's public schools famously rank very poorly, and there is a stron…

So your problem is that these individual students weren’t oppressed enough to warrant an educator’s broader generalization that all students shouldn’t be held back by their many and varied forms of barriers? If you recognize that there’s a vast set of intersecting disadvantages, why would you want to turn it into Oppression Olympics? It’s fine to recognize that not all of those power dynamics might be in play in this…

The articles’s author does not say that “students shouldn’t be held back”.

He says:

“This is just an awesome turn of events and one which should inspire anyone — no matter what their gender, ethnic or socio-demographic background — that excellence in your chosen field of study is always attainable”

“Inspire”. A child who is abused or malnourished or whose caregivers care little or nothing about their education or whose classroom is constantly disrupted by other children living in terrible situations and whose teachers are overworked with large class sizes and incapable of providing them with a proper education (“no matter their socio-demographic background”) will find little to be inspired in this story (if they know the full story that is), regardless of their ethnicity or gender.

Read the comment I initially replied to and see how it interprets the article’s quote as a message of empowerment about “gender/ethnicity” only. It could have been. All the author had to do was remove the “and regardless of socio-demographic background”. As I stated in my initial comment.

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

#279

Post by eyelidlessness »

pedrosorio wrote: post #278
eyelidlessness wrote: post #276

Earlier quoted context omitted.

So your problem is that these individual students weren’t oppressed enough to warrant an educator’s broader generalization that all students shouldn’t be held back by their many and varied forms of barriers? If you recognize that there’s a vast set of intersecting disadvantages, why would you want to turn it into Oppression Olympics? It’s fine to recognize that not all of those power dynamics might be in play in this…

The articles’s author does not say that “students shouldn’t be held back”. He says: “This is just an awesome turn of events and one which should inspire anyone — no matter what their gender, ethnic or socio-demographic background — that excellence in your chosen field of study is always attainable” “Inspire”. A child who is abused or malnourished or whose caregivers care little or nothing about their education or who…

I’ve been a child in several of the situations you describe, so I have little reason to speculate about how I would react, and I think you’re engaging this whole discussion in the worst faith possible to find much greater fault in a statement, which itself is a pretty milquetoast blanket wish for students to succeed without artificial barriers. You’re parsing a thing so far out of its intended context that it can’t help but be absurd, because it doesn’t have any tether to the idea the person expressed at all.

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

#280

Post by pedrosorio »

eyelidlessness wrote: post #279
pedrosorio wrote: post #278

Earlier quoted context omitted.

The articles’s author does not say that “students shouldn’t be held back”. He says: “This is just an awesome turn of events and one which should inspire anyone — no matter what their gender, ethnic or socio-demographic background — that excellence in your chosen field of study is always attainable” “Inspire”. A child who is abused or malnourished or whose caregivers care little or nothing about their education or who…

I’ve been a child in several of the situations you describe, so I have little reason to speculate about how I would react, and I think you’re engaging this whole discussion in the worst faith possible to find much greater fault in a statement, which itself is a pretty milquetoast blanket wish for students to succeed without artificial barriers. You’re parsing a thing so far out of its intended context that it can’t h…

Thanks for the feedback.
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