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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

#71

Post by dang »

KRAKRISMOTT wrote: post #4
oceansea wrote: post #3

[flagged]

Excellent points, I am not sure why you were flagged as dead.

It was an obvious flamewar comment, which is against the site rules, plus name-calling, which is also against the site rules, plus nitpicking in an aggressive way. That's not what HN is for.

https://news.ycombinator.com/newsguidelines.html

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

#72

Post by dang »

oceansea wrote: post #3

[flagged]

You took this thread on an offtopic flamewar tangent, which breaks the site guidelines. We ban accounts that make a habit of this, so please don't do it again.

You also threw in nasty regional flamebait and crude name-calling. Those things are also not allowed here.

If you'd please review https://news.ycombinator.com/newsguidelines.html and stick to the rules when posting to HN, we'd appreciate it.

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

#74

Post by SamReidHughes »

scythe wrote: post #52
joe_the_user wrote: post #20

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…

Induction isn't so bad. I'm not sure how they're getting away with the Law of Sines, though. The usual proof of LoS that I know is dependent on the existence of the circumcircle. But I don't know how to prove the existence of the circumcircle without dragging in a lot of geometry. Or you can use the area formula, which makes the proof similar to other arguments that use the area formula.

There is a very straightforward proof that involves dropping an altitude.

https://www.mathopenref.com/lawofsinesproof.html

You could use a similar technique to make this proof not reference trigonometric functions.

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

#77

Post by Jun8 »

Jarmsy wrote: post #68
threatofrain wrote: post #63

Earlier quoted context omitted.

The article itself says it's not new.

Where does it say that?

“However, this point of view has been increasingly questioned in recent decades, and a few trigonometric proofs of Pythagoras have made the rounds since then. Claims in the media that Johnson and Jackson’s proof is the first trigonometric proof of Pythagoras are overblown, but their proof could well be the most beautiful and simplest trigonometric proof we have seen to date”

my understanding from this part is that their general approach is not new (though certainly astonishing for HS students) but their proof is novel.

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

#79

Post by starchild_3001 »

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 step is ok. https://en.wikipedia.org/wiki/Law_of_sines

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