/sci/ - Science & Math » Thread #11847298

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Can it be done?

Anonymous Sun 28 Jun 20:36:20 2020 No.11847298 View Reply Original Report

Quoted By: >>11847365 >>11847861

Connect A to A, B to B, and C to C without going outside the circle or crossing any lines. Does anybody else know of any problems like this that can be solved/made easier with deformation?

Anonymous

View Same Google iqdb SauceNAO 7716B7FD-D4BF-4910-9CF5-E5383A6D (...).png, 94KiB, 1024x838

Anonymous Sun 28 Jun 2020 20:53:22 No.11847365 Report

Quoted By: >>11847614 >>11849580

>>11847298
done, at least post a difficult one

Anonymous

View Same Google iqdb SauceNAO deformationstep1.png, 20KiB, 640x576

Anonymous Sun 28 Jun 2020 21:42:44 No.11847614 Report

Quoted By: >>11847868

>>11847365
Correct. Not sure if you noticed, but the topology comes in if you when you realize that this is the same problem in an easier form, and you just slide the interior points around to get the answer.

Anonymous

View Same Google iqdb SauceNAO deformationstep2.png, 20KiB, 640x576

Anonymous Sun 28 Jun 2020 21:44:18 No.11847618 Report

Quoted By: >>11847642

"intermediate" step.

Yeah, I was looking for more problems like this to impress my friends. So if anyone knows any...

Anonymous

Anonymous Sun 28 Jun 2020 21:49:04 No.11847642 Report

Quoted By: >>11847793

>>11847618
didn't you ever draw mazes as a kid? just draw any maze and reverse engineer the walls out

Anonymous

Anonymous Sun 28 Jun 2020 22:32:26 No.11847793 Report

Quoted By:

>>11847642
Yeah, that's a good idea. I was thinking more of examples that demonstrated different ideas in Topology, so I could go around spewing the "math is easy and cool" narrative that I like push for some reason.

Anonymous

Anonymous Sun 28 Jun 2020 22:48:04 No.11847861 Report

Quoted By: >>11847894

>>11847298
https://youtu.be/8YDw4YxT-FM?t=55

Anonymous

Anonymous Sun 28 Jun 2020 22:49:53 No.11847868 Report

Quoted By: >>11847949

>>11847614
I'm betting one hundred dollars that you can't explain what "the topology comes in" in rigorous terms

Anonymous

Anonymous Sun 28 Jun 2020 22:59:00 No.11847894 Report

Quoted By:

>>11847861
Thanks. This series is where I got the problem from, as you probably figured. I was looking to build on his methods to maybe target people with like a high school level of math education. Since that's the demographic I live around.

Anonymous

Anonymous Sun 28 Jun 2020 23:14:11 No.11847949 Report

Quoted By: >>11848046 >>11848056

>>11847868
blah, blah, blah, continuous, blah, blah, bijection, blah, blah, inverse mapping, blah, blah, isomorphic.
I think your missing the point friend, I'm trying to make it appealing to folks that haven't studied any advanced math.

Anonymous

Anonymous Sun 28 Jun 2020 23:47:44 No.11848046 Report

Quoted By: >>11848057

>>11847949
>I think your missing the point friend, I'm trying to make it appealing to folks that haven't studied any advanced math.
I know I'm just fucking with you. but I'm still convinced you can't lol

Anonymous

Anonymous Sun 28 Jun 2020 23:51:28 No.11848056 Report

Quoted By:

>>11847949
It was not his point. Can you or not fag

Anonymous

Anonymous Sun 28 Jun 2020 23:51:35 No.11848057 Report

Quoted By: >>11848173 >>11848829

>>11848046
ahaha. And I'm still not convinced you would know if it's correct if I did. How about showing me how it's done?

Anonymous

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Anonymous Sun 28 Jun 2020 23:52:27 No.11848060 Report

Quoted By: >>11848134 >>11848160 >>11848319 >>11848365

Try this It's not too hard

Anonymous

View Same Google iqdb SauceNAO IMG_20200622_153949.jpg, 25KiB, 232x280

Anonymous Mon 29 Jun 2020 00:12:14 No.11848134 Report

Quoted By: >>11848268

>>11848060
This is easy
I bet you dont know how to do it and want to be spoonfed
Not today mate.

Anonymous

Anonymous Mon 29 Jun 2020 00:16:15 No.11848160 Report

Quoted By:

>>11848060
Just give me a sledge hammer to put 4 "doors" on every cell except the endpoints, and no problem! Actually, I do like this problem. Thanks for posting.

Anonymous

Anonymous Mon 29 Jun 2020 00:18:25 No.11848173 Report

Quoted By: >>11848221 >>11848303 >>11848829

>>11848057
I'm trying to come up with a proof which doesn't use the fact that any homeomorphism between the set of interior points extends to a homeomorphism of the whole disc fixing the boundary, otherwise it's too easy. any ideas ?

Anonymous

Anonymous Mon 29 Jun 2020 00:30:56 No.11848221 Report

Quoted By: >>11848829

>>11848173
Hmmm. Good question. How about assuming they have to intersect, then disprove using intersection theory? I'll think on it while and let you know if I come up with anything.

Anonymous

Anonymous Mon 29 Jun 2020 00:44:06 No.11848268 Report

Quoted By: >>11848338

>>11848134
shit you got me better post the solution before I look like an idi... Ooooo you're a sneaky one anon I'll give you that

Anonymous

Anonymous Mon 29 Jun 2020 00:54:02 No.11848303 Report

Quoted By:

>>11848173
Yeah, intersection theory works I think. I don't want to spoil your fun, but this video pretty much explains how if you're curious.

https://www.youtube.com/watch?v=PrOKlcBu4mA&list=PLTBqohhFNBE_09L0i-lf3fYXF5woAbrzJ&index=17

Anonymous

View Same Google iqdb SauceNAO pokemon ice puzzle.jpg, 26KiB, 480x360

Anonymous Mon 29 Jun 2020 00:59:02 No.11848319 Report

Quoted By: >>11848330

>>11848060
this was literally one of the ice puzzles in pokemon ruby/sapphire. If you can't do this, you're admitting you're dumber than a child

Anonymous

Anonymous Mon 29 Jun 2020 01:03:25 No.11848330 Report

Quoted By:

>>11848319
Pokemon stole the idea from the Zelda gameboy games, just to be clear.

Anonymous

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Anonymous Mon 29 Jun 2020 01:06:41 No.11848338 Report

Quoted By:

>>11848268

Anonymous

Anonymous Mon 29 Jun 2020 01:15:03 No.11848365 Report

Quoted By: >>11848377

>>11848060
So you can do 13>9>13 right? Since we assume there is no one alive in 13.
If yes, then do so, fill up bottom in zigzag, you end up to the side. Go one cell up, now you are one below 4. Go far left, up and far right and we are done. Another solition is same as this one but symmetric by the diagonal from 13 to 4.
If we are not allowed to go back to 13 after visiting 1 cell, i dont know.

Anonymous

Anonymous Mon 29 Jun 2020 01:18:44 No.11848377 Report

Quoted By: >>11848433

>>11848365
I think it's impossible without going through 13 twice. Sorta like the seven bridges problem.

Anonymous

Anonymous Mon 29 Jun 2020 01:37:10 No.11848433 Report

Quoted By: >>11848449 >>11850365

>>11848377
I think i get it why, there are 16 vertices. You could split them in bipartite way (take every second diagonal line from upper right to lower left of cells to one category), doing that 13 and 4 will end up in one category. But n the number of vertices is even, so the path will end in another category.

Anonymous

Anonymous Mon 29 Jun 2020 01:40:25 No.11848449 Report

Quoted By:

>>11848433
Yeah, I think that's sounds right.

Anonymous

View Same Google iqdb SauceNAO 1593018345029m.jpg, 95KiB, 1016x1024

Anonymous Mon 29 Jun 2020 04:01:28 No.11848829 Report

Quoted By: >>11848935 >>11850683

>>11848057
>>11848173
>>11848221
I've never even heard of interesection theory, but it sounds cool.

If we had a lemma that says you can swap any two points in the same partition a connected space and the separation properties of all the paths and loops stay the same, then we can just swap B and C in the original picture. I don't know if that makes sense or if it's correct because I don't really know algebraic topology yet, but it seems like a plausible property.

Anonymous

Anonymous Mon 29 Jun 2020 04:31:26 No.11848935 Report

Quoted By:

>>11848829
I haven't seen that lemma, but it does seem to fit this situation as well. I think we got this figured out!

Anonymous

Anonymous Mon 29 Jun 2020 09:58:46 No.11849580 Report

Quoted By:

>>11847365
fking genius

Anonymous

Anonymous Mon 29 Jun 2020 16:29:50 No.11850365 Report

Quoted By: >>11852096 >>11852100

>>11848433
not sure about your solution can you explain it to me like I'm 4 please?

Anonymous

Anonymous Mon 29 Jun 2020 18:36:31 No.11850683 Report

Quoted By: >>11850688

>>11848829
all connected smooth manifolds of dimension at least 2 are n-homogenous: for every bijection between two n-tuples of points there exists a diffeotopy which brings the first tuple onto the second tuple according to the bijection. it's a special case of the isotopy theorem which says that every isotopy of a compact submanifold extends to a diffeotopy (fixing the boundary and with compact support if the manifold is not closed) of the whole manifold.

Anonymous

Anonymous Mon 29 Jun 2020 18:38:52 No.11850688 Report

Quoted By:

>>11850683
*in case you don't know, diffeotopy means homotopy of the identity through diffeomorphisms, so literally all topological properties remain unchanged

Anonymous

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Anonymous Tue 30 Jun 2020 02:14:17 No.11852096 Report

Quoted By: >>11852897

>>11850365
You have green group and blue group of cells. Each green cell is connected to blue one and vice versa and no blue is connected with blue, and same is true for green (this is thw bipartite graph stuff). Now when we would like to pass through every cell just once, it implies if we start at green, we finish at blue, because every pass from cell to cell switches you to cell of another color. To reach any second cell, you havebto go green > blue.
To 4th: g>b>g>b.
So to complete any path of even number of cells, we end at blue. the required path consists of 16 cells, so you cannot end at green if you stick to the rules. And the end point is green so its not possible.

Anonymous

View Same Google iqdb SauceNAO IMG_20200630_041713.jpg, 369KiB, 1221x1678

Anonymous Tue 30 Jun 2020 02:17:55 No.11852100 Report

Quoted By:

>>11850365
And the first solution that i asked if you can go back to 13 is this

Anonymous

Anonymous Tue 30 Jun 2020 09:56:25 No.11852897 Report

Quoted By:

>>11852096
very elegant thanks

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