/gtg/ - geometry and topology general

[Anonymous No.11431269]

/mg/ has been absolutely horrendous lately. Hopefully I won't have a reason to make these soon.

[Anonymous No.11431468]

Where do angles come from? Can sine be derived from Pythagoras' theorem?

[Anonymous No.11431563]

>>11431468
>Where do angles come from?
plane geometry
>Can sine be derived from Pythagoras' theorem?
Some identities depend on Pythagoras' theorem. Not sure what you mean derive it, it's just a function.

[Anonymous No.11431570]

>>11431563
dumb answers, kid
that was a test- I'm not posting in your brainlet thread ever again

[Anonymous No.11431592]

>>11431269
Thoughts on rudins chapter into basic topology?
To me its weird as the proofs are either insanely simple or completely esoteric, how do I git gud at this?
I also don't see how this connects to the broader topic of analysis.
Why was there a need to define what a compact set is and why is the definition like that? Seems pretty arbitrary.

[Anonymous No.11431616]

>>11431592
To be clear im not claiming the definition is arbitrary, it clearly isnt, its just that right now, as I don't know its purpose or motivation it seems arbitrary

[Anonymous No.11431648]

>>11431468
>where do angles come from
[math]\mathfrak{so} (2)[/math]
>Can sine be derived from Pythagoras' theorem?
No, you'll need triangle similarity.
>>11431570
That wasn't me, tho.

[Anonymous No.11431665]

>>11431269
bump

[Anonymous No.11431749]

>>11431665
how would you define that shape in topology?

[Anonymous No.11431770]

>>11431749
2-torus? I mean it's pretty obvious

[Anonymous No.11431776]

>>11431749
The oriented manifold with genus 2?

[Anonymous No.11431787]

>>11431770
>>11431776
And what if there's a torus that goes through each hole. What then, nerds?

[Anonymous No.11431797]

>>11431787
That's homeomorphic to the disjoint union of the picture thing and a torus, tho.
I think you might be mixing up isotopy and homeomorphisms.

[Anonymous No.11431807]

>>11431616
whole general topology and ESPECIALLY the notion of compact sets feels extremely unmotivated at first, that's just the way it is. don't worry about it and just keep doing math and you will appreciate it eventually.

[Anonymous No.11431812]

>>11431797
Listen here, you pathetic nerd, I'm ASKING you what you would call A TORUS that goes through EACH HOLE in your pic related. I want to know WHAT you would call that in your MATHS MUMBO JUMBO. Think you've got that, pencil neck?

[Anonymous No.11431849]

>>11431812
The disjoint union of the oriented manifold with genus 2 and the torus.

[Anonymous No.11431978]

>>11431269
If any pair of lines intersect at a point on the line at infinity, then the pair of lines are parallel.

[Anonymous No.11432005]

>>11431978
They intersect at infinity and thus they don't intersect in the affine plane, yes. What's your point?

[Anonymous No.11432199]

>>11431849
Alright, now we're getting somewhere. Now can you specify surface level constraints? i.e. An inside and an outside where the boundary is immutable.

Let's say pic related's initial state had an inside and an outside as described, what would you call that?

[Anonymous No.11432224]

Is there any intuition behind this proof? Or is it just some arbitrary piece of logic
>map matrix operators into a polynomial
>create a linearly dependent set of vectors corresponding to v, Tv, T^2v, T^3v, etc
>since all complex polynomials have a root, the operator T has an eigenvalue for all complex vector spaces

[Anonymous No.11433750]

Nonono, this thread will only die when I SAY SO

[Anonymous No.11434749]

>>11431776
*oriented surface with genus 2

[Anonymous No.11434775]

>>11433750
Pretty based, if I dare say so.

[Anonymous No.11436059]

>>11431592
This topology was invented to generalize a ton of stuff. It won't make sense until way later. Rudin's treatment is pretty bad too. I recommend Rosenlicht instead.

[Anonymous No.11436359]

>>11431468
It is a very complicated question, actually. But as others said, it is related to similitudes and covering spaces