When You Are A Child, You Solve Equations. We Grown-ups Have To Solve Inequalities.

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! :)

This exactly. It feels as if the brains of my friends flow smoothly towards the shore of certainty through the choppy seas of truth- meanwhile I'm taking a raft.

there's a very specific feeling that makes it difficult to study math in an academic environment when all students around you seem like they're exponentially more intuitive than you in this subject

i hate when i browse math-related tags on this site and half the posts are people ranting about how much they hate her. why are you so mean to my wife

What kind of math are you studying?

math tuition is hell im gonna shoot myself with a gun

You took this photo? I've loved it for a long time!

when people are like “he’s not even attractive you could find a guy that looks like him at any gas station” i’m like….. well you see there’s beauty everywhere actually

“Science, my lad, has been built upon many errors; but they are errors which it was good to fall into, for they led to the truth.”

A Journey to the Center of the Earth - Jules Verne

born to go to beautiful libraries and study, forced to hustle in my room <3

I've been pulled into watching the Gotham Chess recaps of the International Chess Championship and here are my thoughts:

This would make a great pro wrestling story

(hearing him actually recap a chess strategy) oh my god i never want to be good at chess

BASELESS ACCUSATION CHEATING GUY?????

ANAL BEADS CHEATING GUY???????????

Ding nooooooo you can do it I believe in you (I'm kinda cheering for both of them but I'm tickled by the concept of "incumbent champ who is somehow the neurotic underdog")

I REALLY never want to be good at chess

probably the sickos on Ao3 have written rpf about this (they have)

Yes.

Suppose 2n/(n-2) is an integer. Call it k. Then 2n = (n-2)k. But notice also that (n-2)×2 = 2n-4. So 2n is divisible by n-2, and so is 2n-4. So their difference, 4, is also divisible by n-2.

(

To see this, subtract the two equalities above. You'll get 2n - (2n-4) = (n-2)k - (n-2)×2, or, simplifying, 4 = (n-2)(k-2), so 4 is divisible by (n-2)

)

The only (positive integer) factors of 4 are 1, 2, and 4. So n-2 has to be 1, 2, or 4, and thus n has to be either 3, 4, or 6.

The question asks only for positive integers, but it would be a mistake to exclude the negatives. If we take negatives into account also, then -4, -2, and -1 also work, for which we get n to be -2, 0, and 1. And notice here that 1, although reached via a negative, is in fact a positive integer solution.

So the only numbers are 1, 3, 4, 6.

For more information on this, this kind of question comes under a part of math called Number Theory.

Does anyone know if 3, 4, and 6 are the only positive numbers for which 2n/(n-2) is an integer or are there more?

Discovering something new in mathematics and then naming it after Euler just to fuck with people.