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File: can sci do this.png (55 KB, 1332x602)
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time for your brainteaser. I have to admit though, I dont actually know the solution myself. its not homework though, I promise.
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lmao what the fuck are you trying to say
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>>10195170
morph a 2d curve into a 3d curve by wrapping its image around a 3d shape
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http://www.kleinbottle.com/
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>>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.
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>>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?
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>>10195377
Knots don't exist in 4d space
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>>10195379
ok. here, ive been starting from the basic shapes.
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File: wrapping paper.png (49 KB, 1340x930)
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>>10195380
>pic related
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File: how to tie a klein bottle.png (187 KB, 1200x1950)
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>>10195271
>>10195377
>>10195379
so how is this not a knot? if you join both ends then it is stuck to the bottle...
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>>10195271
[\math]\Gamma^\alpha_{\mu\lambda}[/math]
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[math]\Gamma^\alpha_{\mu\lambda}[/math]
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[math]\Gamma^{\alpha_{\mu\lambda}}[/math]
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post

[math] 2^a [/math]

end
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post

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

ok
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Just identify the edges with appropriate twists
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>>10195462
[math] \Gamma^{\alpha}_{\mu \lambda} [/math]
use the god damn tex viewer in the top left of posting
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>>10195698
>tex viewer
wow thats awesome. i never saw that before. this website is so functional but so inacessable to newfags.
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is this a triforce thread now?
[math]\Gamma^{\alpha}_{\mu\lambda}[/math]
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>>10195780
[math]\space[/math] ▲
▲ ▲
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>>10195782
>▲
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>>10195164
>3D curve
>it's actually a 2D surface
Fucking retard
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File: 1523053903757.jpg (89 KB, 890x656)
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>>10195820
a picture of a sphere is in 2 dimensions too, you lame brainlet.



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