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05-03-24 05:15 PM |
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| Main - Posts by Flan |
| Flan |
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Level: 82 Posts: 1055/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by pieguy1372 You cut your wrists. |
| Flan |
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Level: 82 Posts: 1056/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
negative fifty-five, no, fifty-six away. |
| Flan |
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Level: 82 Posts: 1057/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
I don't really care. |
| Flan |
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Level: 82 Posts: 1060/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
A geodesic can mean either:
(a) a point whence curve Q fulfills |Q'| = c, c is nonzero positive. (b) more commonly, a curve which has property (a) for all points. For surfaces, we can also state a geodesic curve as one with acceleration perpendicular to the surface at every point, ie, linearly dependent on the unit normal vector. So a proof that isometries are geodesic-preserving then. Let's assume a geodesic curve E in surface M, and an isometry f from M to N, which maps E to fE. Then it follows that at every point on E, the tangent vector is defined and constant. For brevity, I'm defining T = E', fT = fE'. And T should read T(p), or "T at point p", but again, brevity. |T| = c^2 (The square is just for convenience) T.T = c D(T.T) = D(c), the Ds are exterior differentiation 2(T'.T) = 0, ie, E'' . E' = 0 In plain English, the acceleration vector is perpendicular to the tangent vector, which lies in the tangent space of M (at point p, obviously). And if we apply the isometry f, then fT'.fT = 0, fT.fT = d, ie, |fT| = d^2. fE is a geodesic. QED. |
| Flan |
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Level: 82 Posts: 1061/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by Pac Thank you for your constructive posts. |
| Flan |
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Level: 82 Posts: 1062/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Stop defiling currency.  |
| Flan |
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Level: 82 Posts: 1063/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
It's sunny, as always. =\ |
| Flan |
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Level: 82 Posts: 1067/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Tram |
| Flan |
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Level: 82 Posts: 1068/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by blackhole89 Yeah, I did that with Summon Night 2. |
| Flan |
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Level: 82 Posts: 1071/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Fibonacci sequence? |
| Flan |
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Level: 82 Posts: 1072/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by blackhole89 Yeah, I sort of felt like this in HS. First two years were pretty annoying, third was fun, but last year was awesome. Especially physics. I had Japanese all four years though. |
| Flan |
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Level: 82 Posts: 1073/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Not really, at public universities you can shave off most general requirements, and take whatever courses or graduate in two years or so; at private universities, you'd probably have most interesting classes anyways.
Another note, although partially a byproduct of my interests, specific classes without buzzwords in their title, eg general equilibrium theory, generally seem to be interesting, although the low requirements imply deadbeats who need credit to graduate and other such people might be taking the course. My safe suggestion is to check out the textbooks and professor as well. |
| Flan |
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Level: 82 Posts: 1075/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
I have I am ecstatic about the extreme efficacy of BibTeX. However, life is dismal and the future is bleak, the present agonizing. |
| Flan |
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Level: 82 Posts: 1076/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by blackhole89 I have the stomach flu and wonder what the inversion of a stomach looks like. |
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Level: 82 Posts: 1077/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by Arbe Took you long enough, didn't it? |
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Level: 82 Posts: 1080/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
This seems like a good thing, i.e. efficient decomposition of electronics without the hazard and expense of expensive disposal. |
| Flan |
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Level: 82 Posts: 1081/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by Arbe Drinking age is 21 in the US. =\ Congratulations on successfully advancing one more year. |
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Level: 82 Posts: 1084/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
If such a thread was my only celebratory announcement on my birthday, I would hang myself. |
| Flan |
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Level: 82 Posts: 1085/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
This is another reason to go from liquid cooling to a full-blown moat, incidentally. |
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Level: 82 Posts: 1087/1610 EXP: 5120782 Next: 88445 Since: 02-19-07 Last post: 3612 days Last view: 4601 days |
Posted by Grey Mario Learn how to cook, you slob. |
| Main - Posts by Flan |
© 2005-2023 Acmlm, blackhole89, Xkeeper et al. |
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