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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

#281

Post by TheGigaChad »

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.

[dead]

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

#282

Post by zelphirkalt »

samgtx wrote: post #241
yafbum wrote: post #236

I am puzzled by the article's spin on this, which really centers on the fact that this original proof was authored by two teenage African-American girls from the South , as if the interesting thing here was not so much the proof itself than the idea that there are gifted mathematicians from underrepresented backgrounds and skin colors. In my experience, pretty much in any place and social stratus you might visit, the…

It's telling that your comment is currently 2nd ranked. It comes across generous "there are bright math kids everywhere" but really boils down to "don't talk about how they're black" and "don't talk about how they're women." And finished with "my male friend was disadvantaged, the conversation should be about that." Obviously a large number of the HN crowd agrees with you because these types of comments always land a…

I think many are simply tired of having scientific or mathematical or technological progress updates, that should be about the thing that is actually new, intermingled with political agenda or racism. Not everything needs to be turned into a discussion about race or the disadvantaged. It is not helpful and it is not on-topic. Many people don't like being off-topiced and would rather engage in on-topic discussion.

Articles which put much emphasis on these things are often coming across as racist themselves, because of the underlying meaning "Even a X can do it!" as if it was something unusual that an X actually manged to do whatever the article is about. Often this kind of expressed surprise hints at more racism of the authors of such an article, as it shows, that they still try to establish an associtation between race and ability.

In a way the "we are all people" mindset is less racist than all of the acting surprised about a X being able to do it and focussing on the "they are a X" aspect mindset.

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

#283

Post by chx »

chx wrote: post #277
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?

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).

Sorry I left out the condition of x + y + z = π

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

#284

Post by 4dayworkweek4u »

zelphirkalt wrote: post #282
samgtx wrote: post #241

Earlier quoted context omitted.

It's telling that your comment is currently 2nd ranked. It comes across generous "there are bright math kids everywhere" but really boils down to "don't talk about how they're black" and "don't talk about how they're women." And finished with "my male friend was disadvantaged, the conversation should be about that." Obviously a large number of the HN crowd agrees with you because these types of comments always land a…

I think many are simply tired of having scientific or mathematical or technological progress updates, that should be about the thing that is actually new, intermingled with political agenda or racism. Not everything needs to be turned into a discussion about race or the disadvantaged. It is not helpful and it is not on-topic. Many people don't like being off-topiced and would rather engage in on-topic discussion. Art…

How much of ancient and modern math was developed by group B?

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

#285

Post by CRConrad »

Tao3300 wrote: post #234
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 mistake is seeing this as a constructed thing. Math is already there, we only uncover it. If they revealed a previously unseen chamber in the Great Pyramid or something, you wouldn't say "aw nuts, that overcomplicates our existing knowledge of the structure".

Hey, come to think of it, I'd be perfectly happy with it being the corner of a solid cube[*] of rock ploinked diagonally down into the sand; the whole idea of interior chambers and tunnels does kinda make it feel too fussy, not as clean and sleek as it could be...

___

[*]: Dangit, no, wrong shape.

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

#286

Post by ipince »

camjw wrote: post #193
ipince wrote: post #165

Cool proof, though it doesn't consider the case where a=b. If so, the geometric series is non-converging since the ratio isn't less than 1. Geometrically, the construction wouldn't work because the sides A and C of the large "triangle" would be parallel to each other.

When a = b then the proof of the Pythagorean theorem is trivial so this is the sort of nit-picking that actual mathematicians don't care about.

As a mathematician myself, I beg to differ. Proofs should be rigorous, and at the very least it should warrant a mention of this case.

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

#287

Post by ipince »

tzs wrote: post #258
chengiz wrote: post #211

Earlier quoted context omitted.

How is it trivial?

Note that when a = b we have an equilateral triangle, with area a^2/2. Draw a line from the 90 degree angle to side c, bisecting the 90 degree angle into two 45 degree angles. This divides the original triangle into two smaller triangles. From the fact that the sum of the interior angles of a triangle is 180 degrees, it is not hard to see that the two smaller triangles are both equilateral, with sides of a, c/2, and…

Ok, but those triangles aren't equilateral but isosceles :)
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