[fn-mote]

On one hand, I was ready to be interested.

However, I just cannot get excited about an article with proofs that:

(1) give a different name for methods that use sin(90)=1 vs only working with sine of an acute angle ("cyclometric" vs "trigonometric", ugh)

(2) use "high-powered" methods like convergence of infinite geometric series to prove the Pythagorean theorem

(3) apply the law of sines several times to produce the Pythagorean theorem

I just couldn't give it a chance. Give me a good old fashioned proof by a dissection diagram any day.

[lupire]

No one is obligated to be interested in everything, but I don't understand why you are bragging about your lack of intellectual curiosity about precise mathematical thinking. The difference between triangle trigonometry and unit circle trigonometry is well known to mathematics and important for constructing correct proofs (see the OP's cited Zimba's paper for a recent explanation), and deserves a name for clarity in exposition.

If anything, "trigonometric" is the word they should have avoided, since, even though the word is etymologocally closely associated with triangles as they said, it is also commonly used to refer to exactly the thing they are trying to avoid -- dependency on the Pythagorian theorem, which was the spource of all the confusion and fuss and terrible media reporting when they first published their proof and referred to an ill-defined statement in a 100 year old textbook.

There are hundreds of old proofs of Pythagorean Theorem. I'm sure you can find one that satisfies you. For those of us who enjoy new ideas that push back the intellectual frontier, this paper is very nice.

[throw_pm23]

Note that there were already hundreds of old fashioned proofs, the challenge was exactly to find a new one with the "high powered" methods without circularly referring to the PT, which these two kids achieved.

[erehweb]

Tastes differ. Myself, I think it's fascinating that we can use the convergence of infinite geometric series to prove Pythagorean theorem. And particularly inspiring / interesting that two High School students did this.

[kuhewa]

> "cyclometric"

it's cyclotopic, a term they coined. I suggest the intro section juxtaposing trigonometry vs 'circular' approaches might best be read as guidance as to how interested high school students (their past selves?) might think about the topic rather than a necessary preface for their paper.

[lupire]

I am a college graduate and I found it quite interesting and enlightening. I don't understand the persistent effort some bystanders are making to discredit this work that has met the approval of mathematical professionals.

I also very much enjoyed: "In this section, we verify that our proofs aren’t circular."

[MisterBastahrd]

It's called jealousy. They've got all these big brains and nuanced thoughts and somehow not a one of them accomplished something that got that kind of recognition at that age.

Didn't have the motivation? So what? They did.

The things they did seem obvious? Yes, I bet they do in hindsight. Touch screens on cell phones seem obvious today too.

[Suppafly]

>I don't understand the persistent effort some bystanders are making to discredit this work that has met the approval of mathematical professionals.

I don't try to discredit this stuff, and probably couldn't come up with similar proof myself since I'm not that interested in mathematics in general, but I am personally getting kinda tired of all these "child discovers x" stories where x turns out to either be something this is already well known or it turns out that they've just restated something that was well known in a somewhat trivial way. I'm not saying that's what happened in this case, but it is what happens in most of these sorts of stories that get published anytime it's a slow news day.

[sitkack]

Please give them some slack, they were in high school when they wrote the proofs.

[lupire]

No slack needed. The authors did great work, and they have been assured of that, and PP is embarrassing themself with the kind of middlebrow dismissal that Hacker News guidelines discourage.

[contravariant]

I'm a bit of two minds about this. On the one hand you're quite right, it's impressive work for high school students. What I don't like is how pointing that out feels like an insult, when what I really want to convey is that it's impressive but not entirely beyond ordinary high school students with an interest in mathematics.

And articles like this have been popping up for years (I think about the exact same two students even), and each time I have to decide whether to downplay the scale of their achievement so high school students don't lose hope about achieving something similar, or praise them with the qualifier for high school students because they couldn't be expected to have enough mathematical background to push the boundaries of one of the oldest and most extensively researched parts of modern mathematics.

I can't help but feel that each additional article is just further entrenching the stereotype that you're either a genius at mathematics or not, and is demotivating the students in question, because how on earth are they ever going to top this?