🧵 Untitled Thread
Anonymous at Wed, 6 Mar 2024 14:38:19 UTC No. 16059920
From a commonly used high school geometry textbook. What does /sci/ think of this method of proof?
Anonymous at Wed, 6 Mar 2024 14:40:23 UTC No. 16059923
>>16059920
Nobody except high school kids care about euclidean geometry.
Anonymous at Wed, 6 Mar 2024 14:47:10 UTC No. 16059929
>>16059920
Useless.
High school geometry is boring dogshit.
You don't do real proofs, so you don't get familiar with math you learn later, and gaining any deeper insight is practically impossible for students because they're bombarded with vocabulary and notation.
Anonymous at Wed, 6 Mar 2024 15:33:28 UTC No. 16059986
it's insane how divorced high school math is from actual math, having to waste years doing these irrelevant, dumbed-down problems all while knowing fuck all about even basic predicate logic. School should teach you how to properly formulate mathematical arguments.
Anonymous at Wed, 6 Mar 2024 15:56:13 UTC No. 16060011
>>16059920
absolutely sovlless
Anonymous at Wed, 6 Mar 2024 17:42:55 UTC No. 16060092
>>16059920
>zomg LINES!
Anonymous at Wed, 6 Mar 2024 18:48:50 UTC No. 16060189
>>16059986
This particular textbook is part of an attempt to improve mathematics education by having students go through the process of discovery. How well it accomplishes that is the big question. It probably depends greatly on how well it's taught.
There is a very obvious answer to (d), but to those in the know it should be obvious it can't be a complete proof. After sleeping on it, I see how it could be the starting point for a good proof, and how one might lead students to improve the proof. Of course, you do have to make some assumptions, but those assumptions would be spelled out, and students could be introduced at some point to the cases where the assumptions don't hold. I'll need to look up if there's a teacher's guide, because I could definitely see some teachers just accepting the obvious answer.
Anonymous at Thu, 7 Mar 2024 04:38:35 UTC No. 16060864
>>16060469
English translation
Anonymous at Thu, 7 Mar 2024 04:47:24 UTC No. 16060878
>>16059920
hmmmm i guess i just
>dont know
>dont care
Anonymous at Thu, 7 Mar 2024 13:52:12 UTC No. 16061338
>>16060189
Explain in detail what "obvious" means, as an execise.
Anonymous at Thu, 7 Mar 2024 14:57:30 UTC No. 16061399
>>16061338
The first "obvious" means obvious to me, and probably also to /sci/ readers who are expected to have graduated high school and be reasonably competent. I haven't tried this out with actual high school students, so I'm not sure how obvious it would be to them. There could also be a male/female difference in performance which could perhaps be ameliorated by printing the diagram out on a transparency and letting them test things physically. That said, the "obvious answer" merely states the rigid transformation required, and isn't a complete proof.
I also only noticed now that there is a nasty typo in the exercise. I didn't see it because I knew what transformation they were looking for, but it might confuse someone. Where it says angle "BFC" it should say "BCF".
The second, more dubious, "obvious" may require more knowledge than high school would provide to be "obvious." Basically, if I change a certain famous geometrical axiom, the theorem doesn't hold anymore, but it would still be possible to state the rigid transformation. Therefore, merely stating the rigid transformation can't be a complete proof. By a complete proof I mean something that could be turned into a formal proof without any new insights, only programming-style drudgery.
Anonymous at Thu, 7 Mar 2024 15:00:20 UTC No. 16061400
>>16061399
>I didn't see it because I knew what transformation they were looking for
and also because they marked the angles they were actually talking about in the diagram.
Anonymous at Thu, 7 Mar 2024 15:16:42 UTC No. 16061415
>>16059920
I like it.
>t. Community college physicist
Anonymous at Thu, 7 Mar 2024 17:58:42 UTC No. 16061596
To be more clear: naming the rigid transformation that moves angle CFG so it lands on angle BCF is a good first step toward a proof. But to complete the proof you have to show that the transformation you've named actually does move angle CFG so it lands on angle BCF. And the second step actually requires some thinking. Most high schoolers wouldn't even think it would be necessary to prove this; to them it would be "obvious." But the smart ones could perhaps be coached into working out a proof by contradiction by pointing out ways angle CFG could fail to land on angle BCF. You'd need to use Playfair's axiom or something like it.
A lot of high school geometry textbooks just take
lines parallel -> corresponding angles congruent
as a postulate, and that's perfectly reasonable too. I like it better than the postulate Euclid used.
Anonymous at Thu, 7 Mar 2024 18:01:55 UTC No. 16061601
>>16061399
Any approach that doesn't start by teaching logic is flawed. This is how they make math out to seem like a detached game.
Anonymous at Thu, 7 Mar 2024 18:04:46 UTC No. 16061602
>>16059986
not only is it insane, just image the millions of Chang and Kims that waste 1000+ hours training olympiad level geometry problems like Evan Chen.
Just to end up a washed up 3rd rate mathematician like Po Shen Loh who has to earn their living by selling the competition math training scam to the next generation of gullible idiots.
Anonymous at Thu, 7 Mar 2024 18:08:05 UTC No. 16061605
>>16061602
>Evan Chen
forgot to add pic related
Anonymous at Thu, 7 Mar 2024 18:12:59 UTC No. 16061612
>>16059920
>What does /sci/ think of this method of proof?
I don't like exercises that tell you how you should solve it. "Prove X" is infinitely preferable to "Prove X by..."
Anonymous at Thu, 7 Mar 2024 18:20:59 UTC No. 16061624
>>16061612
Remember that we're talking about high school students that will probably never care about math.
The next best thing is some kind of Socratic exercise but that translates poorly to a textbook.