Earlier quoted context omitted.
I was using Stanford’s definition. https://web.stanford.edu/class/archive/cs/cs103/cs103.1202/l...
That's a misc slideshow from a class, not a formal definition.
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New Orleans teenagers found a new proof of the Pythagorean Theorem
31–40 of 287 posts
Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#32Earlier quoted context omitted.
There's no actual requirement for a proof to give you a "why." The steps just all have to be be logically correct and not accidentally, eg, assume what is to be proven. Lots of proofs are basically unhelpful at giving you a "why," that doesn't disqualify them from being a proof.
I was using Stanford’s definition. https://web.stanford.edu/class/archive/cs/cs103/cs103.1202/l...
"A mathematical proof is an argument that demonstrates why a mathematical
statement is true, following the rules of mathematics."
yes, and?
Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#33Earlier quoted context omitted.
Because they are wrong? Read the article. > to make a proof of it would be to show why a^2 + b^2 = c^2 That's what the article shows as a final step. And it outlines what assumptions are made and how the final step is demonstrated. I have no idea what OP is rambling about.
Yeah, they made a symmetry argument, a series expansion argument, and a law of sines argument. None of those require the Pythagorean Theorem and are all separately proven. There may be a reason that it's wrong (I'm not a mathematician but the article's author is). So, they showed why the sum of squares is true for the hypotenuse of a triangle. It's even an exact proof rather than a limit argument. That I could follow…
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Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#34It would be really interesting to see if this could be applied to other analogous scenarios that are sometimes called Pythagorean theorems, in particular I’m thinking of the Pythagorean Theorem of Information Geometry-
p* = argmin p of P (a set of possible distributions) of D_KL (p||q) (where q is eg your model's distribution)Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#35[flagged]
I have a PhD in math and I have no idea what you are talking about. This is a proof.
Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#36Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#37Earlier quoted context omitted.
It matters when you try and make the point that this case “should inspire anyone — no matter what their ethnic, gender or socio-demographic background“, as the article does
That's not the way I took the article. Rather I took it to mean something slightly different: Your ethnicity and/or gender should not be seen as a barrier to advanced mathematics. There is a nuanced difference there.
I would also take that interpretation if the author didn't explicitly mention "socio-demographic background". They should just leave that one out next time.
Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#38Earlier quoted context omitted.
Excellent points, I am not sure why you were flagged as dead.
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Perhaps this is a chance for some self-reflection on your part? This doesn't seem to be a mean pileon of people hating on you, and its not a particularly charged issue to begin with. You are simply not being clear at all in your argument and then otherwise using this whole thing as a platform to talk about your thoughts on the public education system in Louisiana, and most likely I think some broader thoughts of yours on how kids are just too damn coddled these days. (It should be noted that these students are not in the public education system anyway!)
Maybe just try and reflect on whether you would take such an issue with this if the subjects of it didn't challenge your various implicit assumptions so much?
Or at the very least, attempt to be clearer in your writing. and articulate your arguments. As a champion of life and knowledge, this should really be a priority for you.
Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#39Re: New Orleans teenagers found a new proof of the Pythagorean Theorem
#40Earlier quoted context omitted.
There's no actual requirement for a proof to give you a "why." The steps just all have to be be logically correct and not accidentally, eg, assume what is to be proven. Lots of proofs are basically unhelpful at giving you a "why," that doesn't disqualify them from being a proof.
I was using Stanford’s definition. https://web.stanford.edu/class/archive/cs/cs103/cs103.1202/l...
That definition (as interpreted by you) would appear to, at the very least, preemptively disqualify any proof by exhaustion ("it's true because we brute forced all the possibilities and didn't find any counterexamples"), which is a perfectly valid proof method.
https://en.m.wikipedia.org/wiki/Proof_by_exhaustion
"All the steps are valid but it doesn't explain anything and I'm dissatisfied" is not an argument against a proof's validity. Sometimes the argument is just "A implies B implies C implies D implies E implies P, QED" and as long as you are convinced that each step is valid, you've got to take the proof itself as valid, even if the gestalt isn't satisfying.