/sci/ - Science & Math » Thread #11431269

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/gtg/ - geometry and topology general

Anonymous Sun 01 Mar 17:04:15 2020 No.11431269 View Reply Original Report

Quoted By: >>11431592 >>11431665 >>11431978

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

Anonymous

Anonymous Sun 01 Mar 2020 18:15:33 No.11431468 Report

Quoted By: >>11431563 >>11431648 >>11436359

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

Anonymous

Anonymous Sun 01 Mar 2020 18:42:47 No.11431563 Report

Quoted By: >>11431570

>>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

Anonymous Sun 01 Mar 2020 18:44:55 No.11431570 Report

Quoted By: >>11431648

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

Anonymous

Anonymous Sun 01 Mar 2020 18:49:17 No.11431592 Report

Quoted By: >>11431616 >>11436059

>>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

Anonymous Sun 01 Mar 2020 18:53:29 No.11431616 Report

Quoted By: >>11431807

>>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

Anonymous Sun 01 Mar 2020 19:01:27 No.11431648 Report

Quoted By:

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

Anonymous

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Anonymous Sun 01 Mar 2020 19:04:54 No.11431665 Report

Quoted By: >>11431749

>>11431269
bump

Anonymous

Anonymous Sun 01 Mar 2020 19:27:01 No.11431749 Report

Quoted By: >>11431770 >>11431776

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

Anonymous

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Anonymous Sun 01 Mar 2020 19:32:31 No.11431770 Report

Quoted By: >>11431787

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

Anonymous

Anonymous Sun 01 Mar 2020 19:34:54 No.11431776 Report

Quoted By: >>11431787 >>11434749

>>11431749
The oriented manifold with genus 2?

Anonymous

Anonymous Sun 01 Mar 2020 19:39:54 No.11431787 Report

Quoted By: >>11431797

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

Anonymous

Anonymous Sun 01 Mar 2020 19:43:16 No.11431797 Report

Quoted By: >>11431812

>>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

Anonymous Sun 01 Mar 2020 19:45:53 No.11431807 Report

Quoted By:

>>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

Anonymous Sun 01 Mar 2020 19:46:50 No.11431812 Report

Quoted By: >>11431849

>>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

Anonymous Sun 01 Mar 2020 20:02:14 No.11431849 Report

Quoted By: >>11432199

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

Anonymous

Anonymous Sun 01 Mar 2020 20:43:39 No.11431978 Report

Quoted By: >>11432005

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

Anonymous

Anonymous Sun 01 Mar 2020 20:51:06 No.11432005 Report

Quoted By:

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

Anonymous

Anonymous Sun 01 Mar 2020 21:45:20 No.11432199 Report

Quoted By:

>>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

Anonymous Sun 01 Mar 2020 21:53:36 No.11432224 Report

Quoted By:

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

Anonymous Mon 02 Mar 2020 12:12:26 No.11433750 Report

Quoted By: >>11434775

Nonono, this thread will only die when I SAY SO

Anonymous

Anonymous Mon 02 Mar 2020 20:30:40 No.11434749 Report

Quoted By:

>>11431776
*oriented surface with genus 2

Anonymous

Anonymous Mon 02 Mar 2020 20:43:03 No.11434775 Report

Quoted By:

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

Anonymous

Anonymous Tue 03 Mar 2020 08:52:55 No.11436059 Report

Quoted By:

>>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

Anonymous Tue 03 Mar 2020 12:48:40 No.11436359 Report

Quoted By:

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

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