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/sci/ - Science & Math


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10195164 No.10195164 [Reply] [Original] [archived.moe]

time for your brainteaser. I have to admit though, I dont actually know the solution myself. its not homework though, I promise.

>> No.10195170

lmao what the fuck are you trying to say

>> No.10195179

>>10195170
morph a 2d curve into a 3d curve by wrapping its image around a 3d shape

>> No.10195204

http://www.kleinbottle.com/

>> No.10195271

>>10195164
Its not possible to map from a flat surface to a curved one like that, no matter how many surfaces it has.
What you CAN do however is map two points, that determine a line as the shortest distance between them, from a flat surface onto a curved one, and then find the new shortest distance on the curved surface, which is called the geodesic defined as [math]0 = \frac{d(dx^\alpha d\lambda)} {d\lambda} + \Gamma^\alpha_{\mu\lambda} \frac{dx^\mu} {d\lambda} \frac{dx^\lambda} {d\lambda}[/math] where [math]\Gamma^\alpha_{\mu\lambda}[/math] denotes the Cristoffel Symbol determined by the metric of the curved space.

>> No.10195377

>>10195271
>>10195271
are you saying you couldnt tie yarn through a klein bottle? imagine you had a hanky a pen and a klein bottle. at least some subset of solutions are physically verifiable, no?

>> No.10195379

>>10195377
Knots don't exist in 4d space

>> No.10195380

>>10195379
ok. here, ive been starting from the basic shapes.

>> No.10195382
File: 49 KB, 1340x930, wrapping paper.png [View same] [iqdb] [saucenao] [google] [report]
10195382

>>10195380
>pic related

>> No.10195411
File: 187 KB, 1200x1950, how to tie a klein bottle.png [View same] [iqdb] [saucenao] [google] [report]
10195411

>>10195271
>>10195377
>>10195379
so how is this not a knot? if you join both ends then it is stuck to the bottle...

>> No.10195434

>>10195271
[\math]\Gamma^\alpha_{\mu\lambda}[/math]

>> No.10195440

[math]\Gamma^\alpha_{\mu\lambda}[/math]

>> No.10195447

[math]\Gamma^{\alpha_{\mu\lambda}}[/math]

>> No.10195452

post

[math] 2^a [/math]

end

>> No.10195462

post

[math] \Gamma^{\alpha_{\mu \lambda}} [/math]

ok

>> No.10195690

Just identify the edges with appropriate twists

>> No.10195698

>>10195462
[math] \Gamma^{\alpha}_{\mu \lambda} [/math]
use the god damn tex viewer in the top left of posting

>> No.10195719

>>10195698
>tex viewer
wow thats awesome. i never saw that before. this website is so functional but so inacessable to newfags.

>> No.10195780

is this a triforce thread now?
[math]\Gamma^{\alpha}_{\mu\lambda}[/math]

>> No.10195782

>>10195780
[math]\space[/math] ▲
▲ ▲

>> No.10195814

>>10195782
>▲

>> No.10195820

>>10195164
>3D curve
>it's actually a 2D surface
Fucking retard

>> No.10195889
File: 89 KB, 890x656, 1523053903757.jpg [View same] [iqdb] [saucenao] [google] [report]
10195889

>>10195820
a picture of a sphere is in 2 dimensions too, you lame brainlet.

>>
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