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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

#221

Post by Someone »

camjw wrote: post #200
Someone wrote: post #196

Earlier quoted context omitted.

I don’t see it being trivial. Of course, ‘everybody’ knows the diagonal of the unit square has length √2, but don’t we know that because of the Pythagorean theorem? Can you educate me?

I can! Okay so take the triangle made by taking the diagonal of the unit square. This has side lengths 1, 1, and c and has area 1/2. Now, take four of these and arrange them in a square with the side length being c. It would be easier to draw this... basically you stick the right angles in the center. If this isn't clear I can draw a diagram. Anyway, you just made a square with side length c but since its made of fou…

Thanks. Not the same as the 1st proof in https://socratic.org/questions/what-is-one-method-for-provin..., but still reminds me of it.

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

#222

Post by kibwen »

cabalamat wrote: post #209
jonahx wrote: post #99

Earlier quoted context omitted.

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.…

> It's a very clever proof. Which makes it a bad one, IMO. In maths, as in programming, one should go with the simplest way that works.

The Pythagorean theorem is the most frequently re-proved thing in the history of math, with hundreds of published proofs and entire books dedicated to collecting them. The reason to come up new proofs these days is solely for the novelty, not because we have a need for a simpler proof. The fact that it's such a popular subject for proofs is why novel proofs are inherently interesting, regardless of their complexity.

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

#223

Post by briandear »

krick wrote: post #158
no_butterscotch wrote: post #90

[flagged]

> doubtful that this isn't a "cause celebre" sort of situation I mean, honestly… it just is. Is it a new proof? I believe that it is. Is it any good? Yeah, sure, it's pretty clever. Is it really an all-over-the-news special kind of achievement? No. It simply wouldn't be all over the news if not for… uh, non-mathematical reasons. Allegedly it's special, because it's trigonometric, and trigonometric proofs of it are in…

If it were two kids from New York, would the story be “New York teenagers do x?”

The reason the framing rubs me the wrong way is because it feeds a narrative that people from New Orleans (regardless of race) are somehow novel for doing something fancy. I was born in New Orleans so I have some slight offense at the implication that the geography is somehow notable. It’s like “oh wow, even people from some Southern flyover city can do some smart stuff too.”

However what is interesting about this story is the girls go to St Mary’s which is a catholic school created for black people during the segregation era founded by an the second oldest order of American black nuns just after the Civil War. The history of the school is fascinating.

Imagine if more kids had the opportunity to go to high quality private schools but can’t due to financial constraints (St Mary’s costs about $9k per year which is a lot of money for those in Louisiana.)

These girls can write their own ticket now — I hope they end up staying in math and do something extraordinary with their lives.

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

#224

Post by briandear »

ummonk wrote: post #155
sbelskie wrote: post #82

Earlier quoted context omitted.

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!

I see tuition of several thousand (e.g. 7,800 for 8-11th grade): https://smaneworleans.com/tuition-fees Still quite a steal as private schools go, and significantly less than one would have to pay in yearly rent / mortgage to get their kids into a good school district.

It’s a “steal” if you make California wages. For Louisiana, that’s a lot of money. The median home price in New Orleans is roughly $230k — in Santa Clara county, CA, it’s $1.3 million. That makes the tuition comparable to $45k per year which is more expensive that the best private schools in Silicon Valley.

The math is sloppy, but the point is that the tutoring isn’t really a “steal.”

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

#225

Post by camjw »

Someone wrote: post #221
camjw wrote: post #200

Earlier quoted context omitted.

I can! Okay so take the triangle made by taking the diagonal of the unit square. This has side lengths 1, 1, and c and has area 1/2. Now, take four of these and arrange them in a square with the side length being c. It would be easier to draw this... basically you stick the right angles in the center. If this isn't clear I can draw a diagram. Anyway, you just made a square with side length c but since its made of fou…

Thanks. Not the same as the 1st proof in https://socratic.org/questions/what-is-one-method-for-provin... , but still reminds me of it.

Yes this is essentially a special case where the yellow square has side length 0.

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

#226

Post by jonahx »

boycott-israel wrote: post #182
jonahx wrote: post #150

Earlier quoted context omitted.

I address this in my OP. If you watch the video of the proof, you will see that the "law of sines" is 1 step away from the ratio definition of sin. You just drop one altitude, apply the definition again to the similar triangles, and re-arrange. It is almost content free as a result -- I see no reason using this in a proof would have special significance. For example, the standard proof using similar triangles ( https…

Not at all - the hype part is that 2 teenagers derived a uniquely elegant proof that other highly-trained mathematicians had thus far failed to do so. Any other claims seem to have been added by the media, not the teenagers themselves.

That is what I was referring to. I wasn’t accusing the teenagers of anything.

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

#227

Post by sbelskie »

ummonk wrote: post #155
sbelskie wrote: post #82

Earlier quoted context omitted.

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!

I see tuition of several thousand (e.g. 7,800 for 8-11th grade): https://smaneworleans.com/tuition-fees Still quite a steal as private schools go, and significantly less than one would have to pay in yearly rent / mortgage to get their kids into a good school district.

Ahh, the tuition was cut off on mobile and did not realize there was horizontal scroll.

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

#228

Post by cabalamat »

iamerroragent wrote: post #212
cabalamat wrote: post #209

Earlier quoted context omitted.

> It's a very clever proof. Which makes it a bad one, IMO. In maths, as in programming, one should go with the simplest way that works.

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.

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

#229

Post by chengiz »

camjw wrote: post #215
chengiz wrote: post #211

Earlier quoted context omitted.

How is it trivial?

Commented this on another thread: Okay so take the triangle made by taking the diagonal of the unit square. This has side lengths 1, 1, and c and has area 1/2. Now, take four of these and arrange them in a square with the side length being c. It would be easier to draw this... basically you stick the right angles in the center. If this isn't clear I can draw a diagram. Anyway, you just made a square with side length…

You're using geoemetrical construction not dissimilar from proving the theorem for a != b. So it's not in the spirit of this new method. No one disputes there are easier methods to prove the theorem.

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

#230

Post by TuringTest »

kibwen wrote: post #222
cabalamat wrote: post #209

Earlier quoted context omitted.

> It's a very clever proof. Which makes it a bad one, IMO. In maths, as in programming, one should go with the simplest way that works.

The Pythagorean theorem is the most frequently re-proved thing in the history of math, with hundreds of published proofs and entire books dedicated to collecting them. The reason to come up new proofs these days is solely for the novelty, not because we have a need for a simpler proof. The fact that it's such a popular subject for proofs is why novel proofs are inherently interesting, regardless of their complexity.

> The reason to come up new proofs these days is solely for the novelty, not because we have a need for a simpler proof.

On the contrary, every new way to prove a known theorem has the potential to be applicable in other areas of the same or related fields, extending the mathematicians' toolset with new instruments. These new methods often serve as a seed for new discoveries.

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