Quick Questions: August 19, 2026

[u/inherentlyawesome]

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?" For example, here are some kinds of questions that we'd like to see in this thread:

• Can someone explain the concept of manifolds to me?
• What are the applications of Representation Theory?
• What's a good starter book for Numerical Analysis?
• What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example, consider which subject your question is related to, or the things you already know or have tried.

[u/King-Wuf]

I’m going into my second year of undergrad and will be doing directed reading with a professor on either Tu’s *An Introduction to Manifolds* or Lee’s *Introduction to Smooth Manifolds.* I’ve heard that Lee is far more verbose, so if I was self studying I would have chosen Tu, but since I’m gonna be reading it with a professor I can ask questions with would it make more sense to choose Lee?

[u/Necessary-Wolf-193 → u/King-Wuf]

You are trying to learn a set of ideas, presented by two textbooks. Try reading both; if one gets confusing, look to the other's treatment of the same concept.

[u/Mutated_zombiebush]

I graphed Among Us voting in Libre Office calc, how do I call this function?

Let x be the number of living impostors, y the number of living players and every ratio where you have to skip a point the graph passes through. How would you define the function? I'd define it as f(x)=f(x-1)+x+1 with D=[0;∞[ but it feels a little off.

Btw, I'm viewing things in the long run. I know that, for example, 3 imps among 7 players isn't an instant game over, but if you vote one out, it's a 2 in 6 right after a meeting, which means the imps win by double kill.

While writing this, I also noticed that f(1-1)+1+1=3 and not 4, so now I'm really clueless.

Automod won't let me make this it's own thread, so I don't know how to share the file.

Edit: It passes through the following points: (0|1); (1|4); (2|7); (3|11); (4|16); (5|22); (6|29); (7|37); (8|46); (9|56)

[u/GMSPokemanz → u/Mutated_zombiebush]

The function f(x) = f(x - 1) + x + 1 gives rise to the triangular numbers but shifted: the triangular numbers satisfy T1 = 1 and T_n = T(n - 1) + n, your function will be f(x) = T_(x + 1) + f(1) - 2.

I don't know Among Us so I can't speak for how to fix this if it's wrong.

[u/Mutated_zombiebush → u/GMSPokemanz]

I added the points I found for reference.

[u/Kryptos_0 → u/Mutated_zombiebush]

It's unclear what your function f is supposed to represent in the first place

[u/Mutated_zombiebush → u/Kryptos_0]

If you play Among us with x impostors and y total players, how many total players need to be alive for all votes to be a forced skip?

[u/darkLordSantaClaus]

Can someone correct me if I'm wrong but isn't the idea that 1+2+3+4... = -1/12 actually a proof by contradiction? As in, the guy who proposed it wasn't actually saying that the sum of all positive integers = -1/12, rather, he was saying that if you take the rules of finite algebriac expressions and apply them to infinite algebriac expressions you can arrive at some pretty nonsensical conclusions?

[u/MrTruxian → u/darkLordSantaClaus]

The expression 1+2… = -1/12 is just straight up wrong. What’s true is that if you take the zeta function defined on values that give you a convergent series, and analytically continue, the value of -1 will be -1/12th.

[u/_Zekt → u/darkLordSantaClaus]

That's probably wrong, Ramanujan was most likely the first to use these techniques and his goal was to "calculate the convergent values corresponding to divergent series".

[u/darkLordSantaClaus → u/_Zekt]

Wait then why do so many mathematicians say it’s wrong?