You Took This Photo? I've Loved It For A Long Time!

Euclidean Geometry in Mathematical Olympiads

Geometric proofs… might anyone have a good resource for learning them more formally? I need them for a project I’ve recently begun, and hope to find a guide stronger than those reserved for high school geometry courses haha.

Specifically, i’m looking to understand lines, line intersections, things of that type, in a deeper way.

Thank you! :)

math people scare me. math people will be like "math works in mysterious ways TO YOU. i get it though." and they do and it's fucking terrifying.

I remember being in elementary school and feeling a deep alienation at people’s just vicious rejection of mathematics, the reason being, like

It’s like. A classic approach to hypothetical communication with aliens that you start with the things you know you have in common and proceed from there. Mathematics is that.

Imagine you approach someone you don’t understand with a thing specifically designed to be something they and you can agree on as a starting point for communication and they just react with “yeah i hate this”

theyre selling WHAT on ebay now

reading math textbooks means getting insane whiplash when you read the notes in the margins

The cool thing about category theory is that a lot of times I can forget a definition, just think for a minute about what it "should be", and then when I go and look it up I'm right. I've experienced this to a lesser degree in other areas of math but in category theory it seems to come particularly easily.

Things Math Professors Say

"The proof is trivial." (Oh, cool. Guess I’m just an idiot then.)

"Left as an exercise." (Translation: You’ll never solve this in a million years.)

"It’s obvious, really." (Sure, if you’re a demigod.)

"By inspection." (Stares harder at problem… still nothing.)

"For small values of epsilon." (How small? Subatomic? Microscopic? Vibes?)

"WLOG (Without Loss of Generality)." (Oh, we’re just assuming it doesn’t matter now? Alright.)

"Details omitted." (Because apparently, you don’t need to understand it.)

"By the usual argument." (Which you somehow don’t know because you weren’t born in 1702.)

"Assume the rest holds." (That’s some impressive optimism right there.)

"The usual abuse of notation." (Why does this feel like an emotional wound?)

"Almost surely correct." (But also possibly wrong? Cool, thanks for the clarity.)

"A non-rigorous approach." (I thought math was supposed to be precise?!)

"Assume it’s obvious." (Buddy, NOTHING about this is obvious.)

"The reader may verify." (No, the reader may CRY.)

"To the interested reader." (Guess I’m not interested enough, huh?)

"Well-behaved functions only." (We’re function-shaming now?)

"Obvious to the trained eye." (Guess I’ll never make it out of amateur league.)

"A trivial case analysis." (Trivial to WHO??)

"Integrate by parts, twice." (Bold of you to assume I got it the first time.)

"As you can clearly see." (Oh, I clearly see my FAILURE, alright.)

"It works in practice too." (Unlike me, who barely works at all.)

"Assume a spherical cow." (Are we doing math or abstract sculpture?)

"A standard result." (Not in my standards, pal.)

"We skip the tedious algebra." (No, no, please—I wanted to suffer MORE.)

"Assume non-zero solutions exist." (Okay, now we’re just assuming life works out.)

"The usual topology." (Bro, I don’t even know the unusual topology.)

"Finitely many cases left." (Just kidding, there’s 72.)

"By virtue of symmetry." (Virtue? I have none left.)

"Don’t worry about the constant." (The constant is probably my GPA dropping.)

"Assume continuity." (I’m assuming my brain is breaking.)

"Smooth functions only." (Guess I’ll leave, I’m clearly not smooth enough.)

"The simplest non-trivial case." (Simplest? NON-TRIVIAL? Pick a side!)

"Epsilon goes to zero." (Epsilon isn’t the only one losing it.)

"And the rest follows." (Where? Straight to my breakdown?)

ok so this is probably just me being a self-obsessed heartless dumbass but is it me or is it that when you're bad at doing something people just tell you to try harder but if you're REALLY BAD at doing something they say "oh it's [mental illness]" and try to actually give you help. what if i do have a mild version of a thing why shouldnt i get help. at least some. just a crumbe of adderall and empathy plz

Parents (when their child is young): "I know everything. You must obey my every command. The tiniest amount of doubt toward me is considered so disrespectful that I'm justified in hitting you for it.

Parents (when their child is grown): "Please forgive me. I'm only human. There's a lot I didn't know. I tried my best."

A lot of people absolutely fail to distinguish between 'I hate this because I was taught this badly' and 'I hate this because this thing is inherently bad', and I hate it.

you know I absolutely agree with the fact that the education system is fucked and traumatises students. I absolutely agree with the fact classes like english and maths and history can be piss boring and teach you nothing of worth and could be a trigger depending on how hellish of a teacher you were given.

Hell, the only reason I love maths is because I primarily engaged with it outside of class and found it fun on my own terms. I'm still bitter towards my history teachers for having clear favourites and not engaging half the class.

but like. if you're railing against the *subjects* themselves, refusing to learn any of the basics as an adult, and bringing up how much you hate them at every opportunity? At some point that becomes a problem you have to deal with yourself.

and if you don't, you're going to be the reason this happens again for the next generation.